Question 1

In the context of Stokes' Law, if a sphere of radius $a$ is moving through a fluid with velocity $v$, the viscous drag force $F$ is given by $F = 6\pi \eta a v$. Which of the following modifications would increase the drag force experienced by the sphere?

Accepted Answer

Correct Option: A. Solution: According to Stokes' Law, the drag force $F$ is directly proportional to the radius $a$, the viscosity $\eta$, and the velocity $v$. Increasing the radius of the sphere will increase the drag force.

Question 2

A hydraulic lift uses Pascal's Law to lift a car. If a force of 100 N is applied to a piston with an area of $0.01 \ m^2$, what is the force exerted by a second piston with an area of $0.1 \ m^2$?

Accepted Answer

Correct Option: B. Solution: According to Pascal's Law, the pressure applied to the first piston is transmitted undiminished to the second piston. Therefore, $P_1 = P_2$, which implies $\frac{F_1}{A_1} = \frac{F_2}{A_2}$. Solving for $F_2$, we get $F_2 = F_1 	imes \frac{A_2}{A_1} = 100 \ N 	imes \frac{0.1 \ m^2}{0.01 \ m^2} = 1000 \ N$.

Question 3

According to Stokes' Law, what is the formula for the viscous drag force $F$ on a sphere of radius $a$ moving with velocity $v$ through a fluid of viscosity $\eta$?

Accepted Answer

Correct Option: A. Solution: Stokes' Law states that the viscous drag force $F$ on a sphere is given by $F = 6 \pi \eta a v$, where $\eta$ is the viscosity, $a$ is the radius, and $v$ is the velocity.

Question 4

A liquid drop of radius $1 	ext{ mm}$ is in equilibrium. If the surface tension of the liquid is $0.05 	ext{ N/m}$, what is the pressure difference between the inside and outside of the drop?

Accepted Answer

Correct Option: C. Solution: The pressure difference $\Delta P$ for a liquid drop is given by $\Delta P = \frac{2S}{r}$, where $S$ is the surface tension and $r$ is the radius. Substituting the given values, $\Delta P = \frac{2 	imes 0.05 	ext{ N/m}}{0.001 	ext{ m}} = 100 	ext{ N/m}^2 = 100 	ext{ Pa}$.

Question 5

A raindrop falls through air and eventually reaches a constant velocity. Which of the following forces balance to achieve this terminal velocity according to Stokes' Law?

Accepted Answer

Correct Option: B. Solution: According to Stokes' Law, a raindrop reaches terminal velocity when the gravitational force is balanced by the viscous force and the buoyant force.

Question 6

A capillary tube of radius 0.5 mm is dipped vertically into a container of water. If the surface tension of water is $0.0727 	ext{ N/m}$ and the contact angle is zero, what is the height to which water will rise in the tube? (Density of water = $1000 	ext{ kg/m}^3$, $g = 9.8 	ext{ m/s}^2$)

Accepted Answer

Correct Option: A. Solution: The height of capillary rise is given by $$h = \frac{2S \cos \Theta}{ho g a}$$. With $\Theta = 0$, $\cos \Theta = 1$. Substituting the given values, $$h = \frac{2 	imes 0.0727}{1000 	imes 9.8 	imes 0.0005} = 0.148 	ext{ m}$$.

Question 7

In a hydraulic brake system, the master cylinder has a diameter of $1.0 	ext{ cm}$ and the wheel cylinder has a diameter of $3.0 	ext{ cm}$. If a force of $50 	ext{ N}$ is applied on the master cylinder, what is the force exerted on the wheel cylinder?

Accepted Answer

Correct Option: B. Solution: The force exerted by the wheel cylinder can be calculated using the area ratio: $F_2 = F_1 	imes \left(\frac{d_2}{d_1}ight)^2 = 50 	imes \left(\frac{3}{1}ight)^2 = 450$ N.

Question 8

A tank is filled with water to a height of 10 meters. According to Torricelli's Law, what will be the speed of efflux from a small hole at the bottom of the tank?

Accepted Answer

Correct Option: A. Solution: According to Torricelli's Law, the speed of efflux $v$ is given by $v = \sqrt{2gh}$. Substituting $g = 9.8 	ext{ m/s}^2$ and $h = 10 	ext{ m}$, we get $v = \sqrt{2 	imes 9.8 	imes 10} = 14 	ext{ m/s}$.

Question 9

A hydraulic lift uses Pascal's law to lift a car. If the area of the smaller piston is $0.01 	ext{ m}^2$ and a force of $100 	ext{ N}$ is applied to it, what is the force exerted by the larger piston with an area of $1 	ext{ m}^2$?

Accepted Answer

Correct Option: B. Solution: According to Pascal's law, the pressure applied to the smaller piston is transmitted equally to the larger piston. Thus, $\frac{F_1}{A_1} = \frac{F_2}{A_2}$. Solving for $F_2$, we get $F_2 = \frac{F_1 	imes A_2}{A_1} = \frac{100 	imes 1}{0.01} = 10000$ N.

Question 10

A capillary tube of radius $a$ is placed vertically in a liquid. The liquid rises to a height $h$ in the tube. Which of the following expressions correctly describes the height $h$?

Accepted Answer

Correct Option: A. Solution: The height $h$ to which the liquid rises in a capillary tube is given by $h = \frac{2S \cos 	heta}{ho g a}$, where $S$ is the surface tension, $	heta$ is the contact angle, $ho$ is the density of the liquid, $g$ is the acceleration due to gravity, and $a$ is the radius of the tube.

Question 11

Which of the following statements about surface tension is true?

Accepted Answer

Correct Option: C. Solution: The surface tension of a liquid usually decreases with an increase in temperature.

Question 12

A hydraulic lift raises a platform by $0.5 	ext{ m}$ when the smaller piston is pushed down by $10 	ext{ cm}$. If the area of the smaller piston is $0.02 	ext{ m}^2$, what is the area of the larger piston?

Accepted Answer

Correct Option: A. Solution: The volume displacement must be equal on both sides, so $A_1 	imes h_1 = A_2 	imes h_2$. Solving for $A_2$, we get $A_2 = \frac{A_1 	imes h_1}{h_2} = \frac{0.02 	imes 0.1}{0.5} = 1.0 	ext{ m}^2$.

Question 13

In a pipe with varying cross-sectional area, if the velocity of the fluid increases, what happens to the cross-sectional area according to the equation of continuity?

Accepted Answer

Correct Option: B. Solution: According to the equation of continuity, as the velocity of the fluid increases, the cross-sectional area decreases to maintain a constant flow rate.

Question 14

What is the force per unit length acting at the interface between a liquid and another medium called?

Accepted Answer

Correct Option: B. Solution: Surface tension is the force per unit length acting at the interface between a liquid and another medium.

Question 15

A cylindrical container is filled with water and has a small hole at the bottom. If the height of the water column is 10 m, what is the speed of efflux of water from the hole, assuming the container is open to the atmosphere?

Accepted Answer

Correct Option: A. Solution: According to Torricelli's law, the speed of efflux $v = \sqrt{2gh}$, where $g = 9.8 	ext{ m/s}^2$ and $h = 10 	ext{ m}$. Thus, $v = \sqrt{2 	imes 9.8 	imes 10}$.

Question 16

A fluid flows through a pipe of varying height. At point 1, the pressure is $P_1$, the velocity is $v_1$, and the height is $h_1$. At point 2, the pressure is $P_2$, the velocity is $v_2$, and the height is $h_2$. Which of the following correctly represents Bernoulli's equation for this scenario?

Accepted Answer

Correct Option: A. Solution: Bernoulli's equation for streamline flow is given by $P + \frac{1}{2}ho v^2 + ho gh = 	ext{constant}$, which applies to points 1 and 2.

Question 17

A capillary tube is immersed in water, and the water rises to a height $h$. If the radius of the tube is halved, what happens to the height of the water column?

Accepted Answer

Correct Option: B. Solution: The height of the water column in a capillary tube is inversely proportional to the radius of the tube, $h = \frac{2S \cos 	heta}{ho g a}$. Halving the radius doubles the height.

Question 18

Consider a soap bubble in air. If the surface tension of the soap solution is $0.03 	ext{ N/m}$ and the radius of the bubble is $2 	ext{ cm}$, what is the excess pressure inside the bubble compared to the outside?

Accepted Answer

Correct Option: D. Solution: For a bubble, the excess pressure $\Delta P$ is given by $\Delta P = \frac{4S}{r}$, where $S$ is the surface tension and $r$ is the radius. Substituting the given values, $\Delta P = \frac{4 	imes 0.03 	ext{ N/m}}{0.02 	ext{ m}} = 6 	ext{ N/m}^2 = 6 	ext{ Pa}$. However, since there are two interfaces (inner and outer), the formula becomes $\Delta P = \frac{8S}{r}$, thus $\Delta P = \frac{8 	imes 0.03}{0.02} = 24 	ext{ Pa}$.

Question 19

A swimmer is 10 m below the surface of a lake. If the atmospheric pressure is $1.01 	imes 10^5$ Pa and the density of water is $1000$ kg/m³, what is the pressure on the swimmer?

Accepted Answer

Correct Option: B. Solution: The pressure on the swimmer is calculated using the formula $P = P_a + ho gh$. Substituting the given values: $P = 1.01 	imes 10^5 	ext{ Pa} + 1000 	ext{ kg/m}^3 	imes 9.8 	ext{ m/s}^2 	imes 10 	ext{ m} = 2.01 	imes 10^5 	ext{ Pa}$.

Question 20

A submarine is at a depth of 500 m in seawater. If the density of seawater is $1.03 	imes 10^3 	ext{ kg/m}^3$ and atmospheric pressure is $1.01 	imes 10^5 	ext{ Pa}$, what is the absolute pressure on the submarine?

Accepted Answer

Correct Option: C. Solution: The absolute pressure is given by $P = P_a + ho gh$. Substituting $P_a = 1.01 	imes 10^5 	ext{ Pa}$, $ho = 1.03 	imes 10^3 	ext{ kg/m}^3$, $g = 9.8 	ext{ m/s}^2$, and $h = 500 	ext{ m}$, we get $P = 1.01 	imes 10^5 + 1.03 	imes 10^3 	imes 9.8 	imes 500 = 5.16 	imes 10^6 	ext{ Pa}$.

Question 21

An airplane wing is designed to create lift using Bernoulli's principle. How does the shape of the wing contribute to this lift?

Accepted Answer

Correct Option: C. Solution: The aerofoil shape of the wing causes air to flow faster over the top surface than below, reducing pressure above the wing according to Bernoulli's principle, and generating lift.

Question 22

What is the expression for pressure variation with depth in a fluid?

Accepted Answer

Correct Option: A. Solution: The pressure in a fluid increases with depth due to the weight of the fluid above, described by $P = P_a + \rho gh$, where $P_a$ is the atmospheric pressure, $\rho$ is the fluid density, $g$ is the acceleration due to gravity, and $h$ is the depth.

Question 23

In a hydraulic lift, a small piston with an area of $A_1$ is used to lift a car on a larger piston with an area of $A_2$. If a force $F_1$ is applied to the small piston, what force $F_2$ is exerted on the car?

Accepted Answer

Correct Option: A. Solution: According to Pascal's law, the pressure applied to a confined fluid is transmitted undiminished throughout the fluid. Therefore, $F_2 = F_1 \cdot \frac{A_2}{A_1}$, allowing the lift to exert a larger force on the car.

Question 24

What is the primary factor that determines the viscosity of a fluid?

Accepted Answer

Correct Option: A. Solution: The viscosity of a fluid is primarily affected by temperature. As temperature increases, the viscosity of liquids generally decreases, while the viscosity of gases increases.

Question 25

A small sphere of radius $r$ is falling through a viscous medium with a terminal velocity $v_t$. If the viscosity of the medium is $\eta$, the density of the sphere is $\rho_s$, and the density of the medium is $\rho_m$, which of the following expressions correctly represents the terminal velocity of the sphere according to Stokes' Law?

Accepted Answer

Correct Option: A. Solution: According to Stokes' Law, the terminal velocity $v_t$ of a sphere falling through a viscous medium is given by $v_t = \frac{2r^2(\rho_s - \rho_m)g}{9\eta}$. This expression accounts for the balance of gravitational force, buoyant force, and viscous drag force acting on the sphere.

Question 26

According to Pascal's Law, what happens when pressure is applied to an enclosed fluid?

Accepted Answer

Correct Option: A. Solution: Pascal's Law states that a change in pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and the walls of the containing vessel.

Question 27

What is the effect of temperature on the surface tension of a liquid?

Accepted Answer

Correct Option: B. Solution: Surface tension generally decreases with an increase in temperature because the increased kinetic energy of the molecules reduces the cohesive forces at the surface.

Question 28

In a horizontal pipe with varying cross-section, if the velocity of an incompressible fluid at the narrower section is $4 	ext{ m/s}$, what will be the velocity at the wider section if the cross-sectional area of the narrower section is half of the wider section?

Accepted Answer

Correct Option: A. Solution: According to the equation of continuity, $A_1v_1 = A_2v_2$. If $A_1 = \frac{1}{2}A_2$, then $v_2 = \frac{A_1}{A_2}v_1 = \frac{1}{2} 	imes 4 = 2 	ext{ m/s}$.

Question 29

A liquid rises in a capillary tube to a height of $h$. If the radius of the tube is halved, what happens to the height of the liquid column?

Accepted Answer

Correct Option: B. Solution: The height of the liquid column in a capillary tube is inversely proportional to the radius of the tube. If the radius is halved, the height doubles.

Question 30

What is the SI unit of pressure?

Accepted Answer

Correct Option: A. Solution: The SI unit of pressure is the Pascal (Pa), which is equivalent to $N/m^2$.

Question 31

Which of the following statements about Bernoulli's principle is true?

Accepted Answer

Correct Option: C. Solution: Bernoulli's principle is applicable to incompressible, non-viscous fluids in steady flow, without accounting for energy loss due to viscosity.

Question 32

A cylindrical tank is filled with water up to a height of 10 m. If a hole is made at the bottom, what will be the speed of efflux of water from the hole? Assume the tank is open to the atmosphere and neglect air resistance.

Accepted Answer

Correct Option: A. Solution: The speed of efflux is given by Torricelli's theorem: $v = \sqrt{2gh}$. Substituting $g = 9.8 	ext{ m/s}^2$ and $h = 10 	ext{ m}$, we get $v = \sqrt{2 	imes 9.8 	imes 10}$ m/s.

Question 33

Consider a fluid flowing through a pipe of varying cross-section. At a certain point, the cross-sectional area of the pipe is $A_1$ and the fluid velocity is $V_1$. At another point, the cross-sectional area is $A_2$ and the fluid velocity is $V_2$. Which of the following equations represents the principle of continuity for this fluid flow?

Accepted Answer

Correct Option: A. Solution: The principle of continuity for incompressible fluid flow states that the product of cross-sectional area and velocity remains constant along the pipe: $A_1 V_1 = A_2 V_2$.

Question 34

Consider a fluid flowing through a pipe with varying cross-sectional areas. According to Bernoulli's principle, what happens to the velocity of the fluid as it moves from a wider section to a narrower section of the pipe?

Accepted Answer

Correct Option: C. Solution: According to Bernoulli's principle and the equation of continuity, $A_1v_1 = A_2v_2$, where $A$ is the cross-sectional area and $v$ is the velocity. When the fluid moves from a wider section to a narrower section, the area $A$ decreases, causing the velocity $v$ to increase to maintain the constant flow rate.

Question 35

In an open-tube manometer, if the height difference of the liquid column is $h$ and the liquid density is $\rho$, what is the gauge pressure at the bottom of the liquid column?

Accepted Answer

Correct Option: A. Solution: The gauge pressure at the bottom of the liquid column in an open-tube manometer is given by $P = \rho gh$, where $\rho$ is the density of the liquid and $g$ is the acceleration due to gravity.

Question 36

Which of the following best describes the Magnus effect?

Accepted Answer

Correct Option: A. Solution: The Magnus effect refers to the lift force on a spinning object moving through a fluid, caused by pressure differences due to changes in velocity around the object.

Question 37

In a hydraulic lift, a force $F_1$ is applied to a piston of area $A_1$, which is connected to a larger piston of area $A_2$. What is the force $F_2$ exerted by the larger piston, assuming the fluid is incompressible?

Accepted Answer

Correct Option: A. Solution: According to Pascal's law, the pressure is transmitted undiminished in a hydraulic system: $\frac{F_1}{A_1} = \frac{F_2}{A_2}$. Therefore, $F_2 = F_1 	imes \frac{A_2}{A_1}$.

Question 38

A fluid flows through a pipe with varying cross-sectional areas. If the velocity of the fluid increases at a narrower section, what happens to the pressure at that section according to Bernoulli's principle?

Accepted Answer

Correct Option: B. Solution: According to Bernoulli's principle, if the velocity of the fluid increases, the pressure decreases at that section.

Question 39

A spherical drop of water is in equilibrium. If its radius increases by $\Delta r$, what is the relation between the surface energy and the pressure difference inside and outside the drop?

Accepted Answer

Correct Option: C. Solution: As the radius of the drop increases, the surface area increases, leading to an increase in surface energy. The pressure difference inside and outside the drop is given by $P_i - P_o = \frac{2S}{r}$, which increases as the radius increases.

Question 40

What is the pressure difference between the inside and outside of a spherical drop of radius $r$ due to surface tension $S$?

Accepted Answer

Correct Option: A. Solution: The pressure difference across a spherical drop is given by $\Delta P = \frac{2S}{r}$, where $S$ is the surface tension and $r$ is the radius of the drop.

Question 41

A fluid flows through a pipe that narrows from a cross-sectional area of $0.1 \ m^2$ to $0.05 \ m^2$. If the velocity of the fluid in the wider section is $2 \ m/s$, what is the velocity in the narrower section?

Accepted Answer

Correct Option: C. Solution: Using the equation of continuity, $A_1v_1 = A_2v_2$, where $A_1 = 0.1 \ m^2$, $v_1 = 2 \ m/s$, $A_2 = 0.05 \ m^2$. Solving for $v_2$, we get $v_2 = \frac{A_1v_1}{A_2} = \frac{0.1 \ m^2 	imes 2 \ m/s}{0.05 \ m^2} = 4 \ m/s$.

Question 42

A spherical drop of liquid has a radius $r$. If the radius is doubled, how does the pressure inside the drop change, assuming surface tension $S$ remains constant?

Accepted Answer

Correct Option: C. Solution: The pressure difference across a spherical drop is given by $(P_i - P_o) = \frac{2S}{r}$. If the radius $r$ is doubled, the pressure difference halves.

Question 43

What causes the rise of a liquid in a narrow tube during capillary action?

Accepted Answer

Correct Option: B. Solution: Capillary action is caused by adhesive forces between the liquid and the tube material, along with surface tension.

Question 44

Consider an open-tube manometer connected to a gas tank. The atmospheric pressure is $1.01 	imes 10^5 	ext{ Pa}$, and the difference in mercury levels in the two arms of the manometer is 0.2 m. The density of mercury is $13.6 	imes 10^3 	ext{ kg/m}^3$. What is the absolute pressure of the gas in the tank?

Accepted Answer

Correct Option: C. Solution: The pressure difference due to mercury is $\Delta P = ho gh = 13.6 	imes 10^3 	imes 9.8 	imes 0.2 = 2.67 	imes 10^4 	ext{ Pa}$. Therefore, the absolute pressure of the gas is $P = P_a + \Delta P = 1.01 	imes 10^5 + 2.67 	imes 10^4 = 1.28 	imes 10^5 	ext{ Pa}$.

Question 45

A cylindrical container is filled with water to a height of 10 m. What is the pressure at the bottom of the container due to the water column alone? Assume the density of water is $1000 	ext{ kg/m}^3$ and $g = 9.8 	ext{ m/s}^2$.

Accepted Answer

Correct Option: B. Solution: The pressure due to the water column is given by $P = ho gh = 1000 	imes 9.8 	imes 10 = 98,000 	ext{ Pa}$.

Question 46

A hydraulic lift is used to lift a car weighing 1500 kg. The diameter of the smaller piston is 0.1 m, and the diameter of the larger piston is 0.5 m. If a force of 500 N is applied on the smaller piston, what is the force exerted by the larger piston?

Accepted Answer

Correct Option: A. Solution: Using Pascal's Law, the pressure applied on the smaller piston is transmitted undiminished to the larger piston. The force exerted by the larger piston is given by $$F_2 = F_1 	imes \frac{A_2}{A_1}$$, where $$A_1$$ and $$A_2$$ are the areas of the smaller and larger pistons, respectively. Therefore, $$F_2 = 500 	imes \frac{\pi (0.25)^2}{\pi (0.05)^2} = 12,500 	ext{ N}$$.

Question 47

What is the primary reason that free liquid drops and bubbles are spherical in the absence of external forces like gravity?

Accepted Answer

Correct Option: A. Solution: Free liquid drops and bubbles are spherical because a sphere has the minimum surface area for a given volume, minimizing the surface energy due to surface tension.

Question 48

A cricket ball is bowled with a spin and moves through the air. Due to the Magnus effect, what is the primary reason for the ball's deviation from its expected path?

Accepted Answer

Correct Option: B. Solution: The Magnus effect explains that the spin of the ball drags air with it, creating a pressure difference due to varying velocities of air above and below the ball, resulting in a lift force that deviates the ball's path.

Question 49

A liquid drop tends to acquire a spherical shape due to which property?

Accepted Answer

Correct Option: B. Solution: Surface tension causes a liquid drop to acquire a spherical shape as it minimizes the surface area for a given volume.

Question 50

What does the equation of continuity state for an incompressible fluid flow?

Accepted Answer

Correct Option: A. Solution: The equation of continuity for incompressible fluid flow states that the product of cross-sectional area and velocity remains constant along a streamline.

Question 51

A capillary tube of radius $a$ is inserted into a liquid. If the contact angle is $	heta$, what is the expression for the capillary rise $h$?

Accepted Answer

Correct Option: A. Solution: The capillary rise $h$ is given by the expression $h = \frac{2S \cos 	heta}{ho g a}$, where $S$ is the surface tension, $ho$ is the density of the liquid, $g$ is the acceleration due to gravity, and $a$ is the radius of the tube.

Question 52

A fluid flows through a pipe with varying cross-sectional areas. At a point where the cross-sectional area is $A_1$, the velocity is $v_1$. If the area decreases to $A_2$, what happens to the velocity $v_2$ of the fluid at this point, assuming incompressible flow?

Accepted Answer

Correct Option: A. Solution: According to the equation of continuity, $A_1v_1 = A_2v_2$. Therefore, if $A_2 < A_1$, then $v_2 > v_1$.

Question 53

A cylindrical tank with a cross-sectional area of $A_2$ is filled with water and has a small orifice with cross-sectional area $A_1$ at the bottom. If $A_2 \gg A_1$, what is the speed of efflux from the orifice when the water level is $h$ meters above the orifice?

Accepted Answer

Correct Option: A. Solution: When $A_2 \gg A_1$, the velocity of the water at the surface can be considered negligible. Thus, the speed of efflux $v$ from the orifice is given by $v = \sqrt{2gh}$, according to Torricelli's Law.

Question 54

A spherical raindrop falls through air and eventually reaches a constant velocity. Which of the following statements best explains why the raindrop stops accelerating?

Accepted Answer

Correct Option: B. Solution: As the raindrop falls, its velocity increases until the viscous drag force, given by Stokes' law as $F = 6\pi \eta a v$, becomes equal to the gravitational force. At this point, the net force is zero, and the raindrop reaches terminal velocity, stopping its acceleration.

Question 55

According to Torricelli's Law, what is the speed of efflux of a fluid from an orifice under gravity?

Accepted Answer

Correct Option: A. Solution: Torricelli's Law states that the speed of efflux, $v$, from an orifice is given by $v = \sqrt{2gh}$, where $g$ is the acceleration due to gravity and $h$ is the height of the fluid column above the orifice.

Question 56

A spherical drop of water has a radius of 0.5 mm. If the surface tension of water is $0.0727 	ext{ N/m}$, what is the pressure difference between the inside and outside of the drop?

Accepted Answer

Correct Option: A. Solution: The pressure difference across a spherical drop is given by $$\Delta P = \frac{2S}{r}$$, where $S$ is the surface tension and $r$ is the radius. Substituting the given values, $$\Delta P = \frac{2 	imes 0.0727}{0.0005} = 290.8 	ext{ Pa}$$.

Question 57

A ball is spinning while moving through the air. According to Bernoulli's principle, what is the effect on the pressure distribution around the ball?

Accepted Answer

Correct Option: B. Solution: Bernoulli's principle states that an increase in the speed of the fluid occurs simultaneously with a decrease in pressure. Thus, the side with higher air velocity has lower pressure.

Question 58

A spherical raindrop falls through the air and reaches a constant terminal velocity due to the balance of forces. According to Stokes' Law, which of the following factors does NOT affect the terminal velocity of the raindrop?

Accepted Answer

Correct Option: D. Solution: According to Stokes' Law, the terminal velocity $V_t$ is given by $V_t = \frac{2a^2(\rho - \sigma)g}{9\eta}$, where $a$ is the radius, $\rho$ is the density of the raindrop, $\sigma$ is the density of the fluid, $g$ is the acceleration due to gravity, and $\eta$ is the viscosity of the fluid. The color of the raindrop does not affect its terminal velocity.

Question 59

A capillary tube is inserted into a liquid. If the liquid wets the tube, what will be the shape of the meniscus and the direction of capillary action?

Accepted Answer

Correct Option: A. Solution: When a liquid wets the tube, the meniscus is concave, and due to surface tension, the liquid rises in the capillary tube.

Question 60

In a hydraulic lift, if a small force $F_1$ is applied on a piston of area $A_1$, what force $F_2$ is exerted on a larger piston of area $A_2$?

Accepted Answer

Correct Option: A. Solution: In a hydraulic lift, the force exerted on the larger piston is given by $F_2 = F_1 	imes \frac{A_2}{A_1}$, demonstrating the mechanical advantage provided by the lift.

Question 61

A cricket ball is bowled with a spin. How does the Magnus effect influence its trajectory?

Accepted Answer

Correct Option: B. Solution: The Magnus effect causes the ball to curve in the direction of the spin due to pressure differences created by the varying velocities of air on different sides of the spinning ball.

Question 62

In a horizontal flow of an ideal fluid, if the velocity of the fluid at point A is greater than at point B, what can be inferred about the pressure at point A compared to point B?

Accepted Answer

Correct Option: B. Solution: In a horizontal flow, according to Bernoulli's principle, an increase in velocity results in a decrease in pressure. Therefore, the pressure at point A is lower than at point B.

Question 63

If the pressure at the top of a fluid column is atmospheric pressure and the fluid is in a container open to the atmosphere, what is the speed of efflux from a hole at a height $h$ below the fluid surface?

Accepted Answer

Correct Option: A. Solution: According to Torricelli's Law, the speed of efflux $v = \sqrt{2gh}$ for a fluid exiting a hole in a container open to the atmosphere.

Question 64

What is the terminal velocity of a sphere falling through a viscous medium according to Stokes' law?

Accepted Answer

Correct Option: D. Solution: According to Stokes' law, the terminal velocity $V_t$ is given by $V_t = \frac{2a^2 (p-\sigma)g}{9\eta}$, where $a$ is the radius of the sphere, $p$ and $\sigma$ are the densities of the sphere and the fluid respectively, $g$ is the acceleration due to gravity, and $\eta$ is the viscosity of the fluid. Thus, $V_t$ is directly proportional to the square of the radius of the sphere.

Mechanical Properties of ..

Learning Objectives

Learning Objectives

Revision Notes & Summary

Chapter Notes

Bernoulli's Principle

Equation of Continuity

Pascal's Law

Stokes' Law

Surface Tension

Capillary Action

Pressure Variation with Depth

Viscosity

Dynamic Lift and Magnus Effect

Torricelli's Law

Pressure, Density and Relative Density

Atmospheric Pressure, Gauge Pressure and Manometer

Hydraulic Machines

Streamline, Laminar and Turbulent Flow

Terminal Velocity

Exam Tips & Common Mistakes

Common Mistakes & Exam Tips

Bernoulli's Principle

Equation of Continuity

Pascal's Law

Stokes' Law

Surface Tension

Capillary Action

Pressure Variation with Depth

Viscosity

Dynamic Lift and Magnus Effect

Torricelli's Law

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Practice Test – MCQs, True/False

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Multiple Choice Questions

Q1.In the context of Stokes' Law, if a sphere of radius aaa is moving through a fluid with velocity vvv, the viscous drag force FFF is given by F=6πηavF = 6\pi \eta a vF=6πηav. Which of the following modifications would increase the drag force experienced by the sphere?

Correct Answer: A

Q2.A hydraulic lift uses Pascal's Law to lift a car. If a force of 100 N is applied to a piston with an area of 0.01 m20.01 \ m^20.01 m2, what is the force exerted by a second piston with an area of 0.1 m20.1 \ m^20.1 m2?

Correct Answer: B

Q3.According to Stokes' Law, what is the formula for the viscous drag force FFF on a sphere of radius aaa moving with velocity vvv through a fluid of viscosity η\etaη?

Correct Answer: A

Q4.A liquid drop of radius 1 mm1 \text{ mm}1 mm is in equilibrium. If the surface tension of the liquid is 0.05 N/m0.05 \text{ N/m}0.05 N/m, what is the pressure difference between the inside and outside of the drop?

Correct Answer: C

Q5.A raindrop falls through air and eventually reaches a constant velocity. Which of the following forces balance to achieve this terminal velocity according to Stokes' Law?

Correct Answer: B

Correct Answer: A

Q7.In a hydraulic brake system, the master cylinder has a diameter of 1.0 cm1.0 \text{ cm}1.0 cm and the wheel cylinder has a diameter of 3.0 cm3.0 \text{ cm}3.0 cm. If a force of 50 N50 \text{ N}50 N is applied on the master cylinder, what is the force exerted on the wheel cylinder?

Correct Answer: B

Q8.A tank is filled with water to a height of 10 meters. According to Torricelli's Law, what will be the speed of efflux from a small hole at the bottom of the tank?

Correct Answer: A

Q9.A hydraulic lift uses Pascal's law to lift a car. If the area of the smaller piston is 0.01 m20.01 \text{ m}^20.01 m2 and a force of 100 N100 \text{ N}100 N is applied to it, what is the force exerted by the larger piston with an area of 1 m21 \text{ m}^21 m2?

Correct Answer: B

Q10.A capillary tube of radius aaa is placed vertically in a liquid. The liquid rises to a height hhh in the tube. Which of the following expressions correctly describes the height hhh?

Correct Answer: A

Q11.Which of the following statements about surface tension is true?

Correct Answer: C

Q12.A hydraulic lift raises a platform by 0.5 m0.5 \text{ m}0.5 m when the smaller piston is pushed down by 10 cm10 \text{ cm}10 cm. If the area of the smaller piston is 0.02 m20.02 \text{ m}^20.02 m2, what is the area of the larger piston?

Correct Answer: A

Q13.In a pipe with varying cross-sectional area, if the velocity of the fluid increases, what happens to the cross-sectional area according to the equation of continuity?

Correct Answer: B

Q14.What is the force per unit length acting at the interface between a liquid and another medium called?

Correct Answer: B

Q15.A cylindrical container is filled with water and has a small hole at the bottom. If the height of the water column is 10 m, what is the speed of efflux of water from the hole, assuming the container is open to the atmosphere?

Correct Answer: A

Correct Answer: A

Q17.A capillary tube is immersed in water, and the water rises to a height hhh. If the radius of the tube is halved, what happens to the height of the water column?

Correct Answer: B

Q18.Consider a soap bubble in air. If the surface tension of the soap solution is 0.03 N/m0.03 \text{ N/m}0.03 N/m and the radius of the bubble is 2 cm2 \text{ cm}2 cm, what is the excess pressure inside the bubble compared to the outside?

Correct Answer: D

Q19.A swimmer is 10 m below the surface of a lake. If the atmospheric pressure is 1.01×1051.01 \times 10^51.01×105 Pa and the density of water is 100010001000 kg/m³, what is the pressure on the swimmer?

Correct Answer: B

Q20.A submarine is at a depth of 500 m in seawater. If the density of seawater is 1.03×103 kg/m31.03 \times 10^3 \text{ kg/m}^31.03×103 kg/m3 and atmospheric pressure is 1.01×105 Pa1.01 \times 10^5 \text{ Pa}1.01×105 Pa, what is the absolute pressure on the submarine?

Correct Answer: C

Q21.An airplane wing is designed to create lift using Bernoulli's principle. How does the shape of the wing contribute to this lift?

Correct Answer: C

Q22.What is the expression for pressure variation with depth in a fluid?

Correct Answer: A

Q23.In a hydraulic lift, a small piston with an area of A1A_1A1​ is used to lift a car on a larger piston with an area of A2A_2A2​. If a force F1F_1F1​ is applied to the small piston, what force F2F_2F2​ is exerted on the car?

Correct Answer: A