Question 1

A rigid body is rotating about a fixed axis with an angular velocity $\omega$. If a point on the body at a distance $r$ from the axis has a linear velocity $v$, what is the relation between $v$, $\omega$, and $r$?

Accepted Answer

Correct Option: A. Solution: The linear velocity $v$ of a point on a rotating body is given by the relation $v = \omega r$, where $\omega$ is the angular velocity and $r$ is the distance from the axis of rotation.

Question 2

Consider a system of two particles with masses $m_1$ and $m_2$ connected by a light rod of length $L$. If an external torque is applied perpendicular to the rod, what happens to the angular momentum of the system?

Accepted Answer

Correct Option: B. Solution: An external torque causes a change in angular momentum according to $\frac{dL}{dt} = 	au_{ext}$, where $	au_{ext}$ is the external torque. Thus, the angular momentum increases linearly with time.

Question 3

Which of the following statements about the moment of inertia is correct?

Accepted Answer

Correct Option: A. Solution: The moment of inertia depends on the mass distribution of the body and the axis about which it rotates. It is a measure of the body's resistance to changes in its rotational motion.

Question 4

What is the angular momentum $l$ of a particle with mass $m$, linear momentum $p$, and position vector $r$ relative to the origin?

Accepted Answer

Correct Option: A. Solution: Angular momentum $l$ is defined as the vector product of the position vector $r$ and the linear momentum $p$: $l = r 	imes p$.

Question 5

If a torque $	au$ is applied to a rigid body, which of the following statements correctly describes its effect?

Accepted Answer

Correct Option: B. Solution: Torque $	au$ causes a change in the angular momentum of a body, as given by the relation $\frac{dL}{dt} = 	au$, where $L$ is the angular momentum.

Question 6

In the context of rotational motion, which of the following correctly describes the relationship between torque $	au$ and angular momentum $L$ for a single particle?

Accepted Answer

Correct Option: A. Solution: The relationship between torque $	au$ and angular momentum $L$ for a single particle is given by $\frac{dL}{dt} = 	au$, which is the rotational analogue of Newton's second law.

Question 7

A rigid body is rotating about a fixed axis. Which of the following statements is true about the angular velocity vector $\omega$?

Accepted Answer

Correct Option: C. Solution: For rotation about a fixed axis, the angular velocity vector $\omega$ lies along the axis of rotation.

Question 8

A rigid body is subjected to two forces, $\mathbf{F_1}$ and $\mathbf{F_2}$, which are equal in magnitude but opposite in direction and not collinear. What is the effect of these forces on the rigid body?

Accepted Answer

Correct Option: B. Solution: The forces form a couple, creating a torque that causes rotational motion without translation.

Question 9

Consider a rigid body in equilibrium under the action of several forces. If the net torque about a point on the body is zero, what can be inferred about the forces?

Accepted Answer

Correct Option: C. Solution: For the net torque to be zero, the forces must either be concurrent or their lines of action must intersect at a common point, ensuring rotational equilibrium.

Question 10

Consider a particle moving in a circle with radius $r$ and angular velocity $\omega$. What is the direction of its angular momentum vector?

Accepted Answer

Correct Option: B. Solution: The angular momentum vector is perpendicular to the plane of the circle, following the right-hand rule.

Question 11

A rigid body is in equilibrium under the action of several forces. Which of the following conditions must be satisfied for this equilibrium?

Accepted Answer

Correct Option: C. Solution: For a rigid body to be in mechanical equilibrium, both the sum of all external forces and the sum of all external torques acting on the body must be zero.

Question 12

In the context of rolling motion without slipping, which of the following equations correctly relates linear velocity $v$ and angular velocity $\omega$?

Accepted Answer

Correct Option: A. Solution: For rolling motion without slipping, the linear velocity $v$ is related to the angular velocity $\omega$ by the equation $v = R \cdot \omega$, where $R$ is the radius of the rolling object.

Question 13

A wheel is rotating about a fixed axis with an angular velocity $\omega$. If the radius of the wheel is $r$, what is the linear velocity $v$ of a point on the rim of the wheel?

Accepted Answer

Correct Option: A. Solution: The linear velocity $v$ of a point on the rim of the wheel is given by $v = \omega r$, where $\omega$ is the angular velocity and $r$ is the radius of the wheel.

Question 14

A particle of mass $m$ is moving with a constant velocity $\mathbf{v}$. What is the angular momentum of the particle about a point located at a distance $r$ from the line of motion of the particle?

Accepted Answer

Correct Option: B. Solution: The angular momentum $L$ of a particle about a point is given by $L = r 	imes mv = mvr$, where $r$ is the perpendicular distance from the point to the line of motion.

Question 15

Which of the following conditions must be satisfied for a rigid body to be in mechanical equilibrium?

Accepted Answer

Correct Option: B. Solution: A rigid body is in mechanical equilibrium if the total force and total torque acting on it are zero, ensuring no change in linear or angular momentum.

Question 16

For a rigid body in rotational equilibrium, which of the following conditions must be satisfied?

Accepted Answer

Correct Option: C. Solution: For a rigid body to be in mechanical equilibrium, both the net force and the net torque acting on it must be zero.

Question 17

What is the relationship between torque ($	au$) and angular momentum ($L$) for a single particle?

Accepted Answer

Correct Option: A. Solution: The time rate of change of angular momentum of a particle is equal to the torque acting on it, i.e., $	au = \frac{dL}{dt}$.

Question 18

Consider a uniform L-shaped lamina composed of two identical square plates each of side $a$. The moment of inertia about an axis passing through the center of mass of the lamina and perpendicular to its plane is given by:

Accepted Answer

Correct Option: A. Solution: The moment of inertia of each square about its center is $\frac{Ma^2}{6}$. Using the parallel-axis theorem and symmetry, the total moment of inertia is $\frac{2Ma^2}{3}$.

Question 19

What is the mathematical expression for the center of mass $X$ of a two-particle system with masses $m_1$ and $m_2$ located at positions $x_1$ and $x_2$ respectively?

Accepted Answer

Correct Option: A. Solution: The center of mass $X$ is calculated as the mass-weighted average of the positions: $X = \frac{m_1x_1 + m_2x_2}{m_1 + m_2}$.

Question 20

A particle is moving in a circular path of radius $r$ with a constant speed $v$. If the mass of the particle is $m$, what is the magnitude of its angular momentum about the center of the circle?

Accepted Answer

Correct Option: A. Solution: The angular momentum $L$ of a particle moving in a circle is given by $L = mvr$, where $m$ is the mass, $v$ is the speed, and $r$ is the radius of the circle.

Question 21

What is the torque $	au$ acting on a particle of mass $m$ at position vector $\mathbf{r}$ due to a force $\mathbf{F}$?

Accepted Answer

Correct Option: A. Solution: Torque $	au$ is given by the vector cross product $	au = \mathbf{r} 	imes \mathbf{F}$, where $\mathbf{r}$ is the position vector and $\mathbf{F}$ is the force.

Question 22

Consider two vectors $\mathbf{a} = 3\hat{i} - 4\hat{j} + 5\hat{k}$ and $\mathbf{b} = -2\hat{i} + \hat{j} - 3\hat{k}$. What is the vector product $\mathbf{a} 	imes \mathbf{b}$?

Accepted Answer

Correct Option: A. Solution: The vector product $\mathbf{a} 	imes \mathbf{b}$ is calculated using the determinant form: $\begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 3 & -4 & 5 \ -2 & 1 & -3 \end{vmatrix} = 7\hat{i} - \hat{j} - 5\hat{k}$.

Question 23

Consider a rigid body rotating about a fixed axis. If the angular velocity vector is directed along the axis of rotation, which of the following statements is true?

Accepted Answer

Correct Option: C. Solution: For a rigid body rotating about a fixed axis, the linear velocity of a particle is given by $v = \omega r$, where $\omega$ is the angular velocity and $r$ is the perpendicular distance from the axis of rotation.

Question 24

A cylinder rolls down an inclined plane without slipping. Which of the following statements is true about the point of contact between the cylinder and the plane?

Accepted Answer

Correct Option: B. Solution: In rolling motion without slipping, the point of contact between the rolling object and the surface has zero velocity at any instant.

Question 25

A particle moves in a circle of radius $r$ with constant angular velocity $\omega$. What is the expression for its linear velocity $v$?

Accepted Answer

Correct Option: A. Solution: The linear velocity $v$ of a particle moving in a circle is given by $v = \omega r$, where $\omega$ is the angular velocity and $r$ is the radius of the circle.

Question 26

Which of the following statements about the angular momentum of a particle is correct?

Accepted Answer

Correct Option: C. Solution: Angular momentum is defined as the vector product of the position vector $\mathbf{r}$ and the linear momentum $\mathbf{p}$, i.e., $\mathbf{l} = \mathbf{r} 	imes \mathbf{p}$.

Question 27

A projectile explodes into two fragments in mid-air. What path does the center of mass of the fragments follow?

Accepted Answer

Correct Option: B. Solution: The center of mass of the fragments continues along the same parabolic path that the projectile would have followed if there were no explosion. This is because the internal forces from the explosion do not affect the motion of the center of mass.

Question 28

Consider a binary star system with two stars of equal mass revolving around their common center of mass. If no external forces act on the system, what can be said about the motion of the center of mass?

Accepted Answer

Correct Option: C. Solution: In the absence of external forces, the center of mass of the binary star system moves like a free particle, i.e., in a straight line with constant velocity.

Question 29

A solid cylinder is rolling down an inclined plane without slipping. Which of the following statements is true about its motion?

Accepted Answer

Correct Option: C. Solution: The motion of the cylinder is a combination of translational motion down the plane and rotational motion about its axis.

Question 30

A cylinder rolls down an inclined plane without slipping. Which of the following statements is true regarding its motion?

Accepted Answer

Correct Option: C. Solution: The cylinder exhibits both translational motion down the plane and rotational motion about its axis, as it rolls without slipping.

Question 31

If a particle is moving in a circle of radius $r$ with an angular velocity $\omega$, what is the linear velocity $v$ of the particle?

Accepted Answer

Correct Option: A. Solution: The linear velocity $v$ of a particle moving in a circle is related to the angular velocity $\omega$ by the equation $v = \omega r$.

Question 32

In rotational motion, what is the relationship between linear velocity $v$ and angular velocity $\omega$ for a particle at a distance $r$ from the axis of rotation?

Accepted Answer

Correct Option: A. Solution: The linear velocity $v$ of a particle in rotational motion is given by $v = \omega r$, where $\omega$ is the angular velocity and $r$ is the distance from the axis of rotation.

Question 33

What is the magnitude of the vector product of two vectors $\mathbf{a}$ and $\mathbf{b}$ if the angle between them is $90^\circ$?

Accepted Answer

Correct Option: A. Solution: The magnitude of the vector product is given by $ab \sin \Theta$. When $\Theta = 90^\circ$, $\sin 90^\circ = 1$, so the magnitude is $ab$.

Question 34

Which of the following statements about the center of mass of a system of particles is true?

Accepted Answer

Correct Option: A. Solution: The center of mass of a system of particles moves as if all the mass of the system were concentrated at that point and all external forces were applied there.

Question 35

A projectile explodes into two fragments while in motion. If the explosion is purely internal and no external forces act on the system, what will be the path of the center of mass of the fragments?

Accepted Answer

Correct Option: B. Solution: The center of mass of the fragments will continue along the original parabolic path because the external force (gravity) remains the same before and after the explosion.

Question 36

In a system of particles, the total external force is zero. What can be said about the motion of the center of mass?

Accepted Answer

Correct Option: A. Solution: When the total external force acting on a system of particles is zero, the center of mass moves with constant velocity according to Newton's first law.

Question 37

In the context of rotational dynamics, which of the following statements is true regarding the torque $	au$ acting on a particle?

Accepted Answer

Correct Option: B. Solution: Torque is defined as the vector product $	au = r 	imes F$, where $r$ is the position vector and $F$ is the force. It depends on the angle between $r$ and $F$ and is perpendicular to the plane containing them.

Question 38

A system consists of three particles with masses $m_1 = 2\, 	ext{kg}$, $m_2 = 3\, 	ext{kg}$, and $m_3 = 5\, 	ext{kg}$ located at positions $(1, 0, 0)$, $(0, 2, 0)$, and $(0, 0, 3)$ respectively. What is the $x$-coordinate of the center of mass of the system?

Accepted Answer

Correct Option: A. Solution: The $x$-coordinate of the center of mass is given by $X = \frac{m_1x_1 + m_2x_2 + m_3x_3}{m_1 + m_2 + m_3} = \frac{2 	imes 1 + 3 	imes 0 + 5 	imes 0}{2 + 3 + 5} = 0.5$.

Question 39

What is the moment of inertia of a rigid body primarily dependent on?

Accepted Answer

Correct Option: B. Solution: The moment of inertia is the rotational analogue of mass and depends on the distribution of mass and the axis of rotation.

Question 40

A solid cylinder of mass $M$ and radius $R$ is rolling down an inclined plane without slipping. What is the moment of inertia of the cylinder about its axis of rotation?

Accepted Answer

Correct Option: A. Solution: The moment of inertia of a solid cylinder about its axis is given by $I = \frac{1}{2}MR^2$. This is a standard result for a solid cylinder.

Question 41

A disc of mass $M$ and radius $R$ is rotating about its central axis with angular velocity $\omega$. If a small mass $m$ is placed at the edge of the disc, what is the new angular velocity of the system?

Accepted Answer

Correct Option: A. Solution: Using conservation of angular momentum, $I_{initial} \omega = I_{final} \omega_{new}$, where $I_{final} = MR^2 + mR^2$. Solving gives $\omega_{new} = \frac{M\omega}{M + m}$.

Question 42

Which theorem is applicable when calculating the moment of inertia for a composite body about an axis parallel to an axis through its center of mass?

Accepted Answer

Correct Option: B. Solution: The parallel-axis theorem is used to find the moment of inertia of a body about any axis parallel to an axis through its center of mass.

Question 43

What is the relationship between torque ($	au$) and angular acceleration ($\alpha$) for a rigid body rotating about a fixed axis?

Accepted Answer

Correct Option: A. Solution: The relationship between torque and angular acceleration for a rigid body rotating about a fixed axis is given by $	au = I \alpha$, where $I$ is the moment of inertia.

Question 44

If a rigid body is rotating about a fixed axis, what is the relationship between the linear velocity $v$ of a particle at a distance $r$ from the axis and the angular velocity $\omega$?

Accepted Answer

Correct Option: A. Solution: The linear velocity $v$ of a particle moving in a circle of radius $r$ is related to the angular velocity $\omega$ by the equation $v = \omega r$.

Question 45

In the context of rotational motion, which of the following statements is true regarding the conservation of angular momentum?

Accepted Answer

Correct Option: A. Solution: Angular momentum is conserved if the total external torque on a system is zero, as stated by $L = 	ext{constant}$ when $	au_{	ext{ext}} = 0$.

Question 46

A rigid body is rotating about a fixed axis with an angular velocity $\omega$. If the radius of the circle described by a particle on the body is $r$, what is the linear velocity $v$ of the particle?

Accepted Answer

Correct Option: A. Solution: The linear velocity $v$ of a particle moving in a circle of radius $r$ is given by $v = \omega r$, where $\omega$ is the angular velocity.

Question 47

A solid cylinder rolls without slipping down an inclined plane. If the linear velocity of the center of mass of the cylinder is $v$, what is the angular velocity $\omega$ of the cylinder?

Accepted Answer

Correct Option: A. Solution: For rolling without slipping, the relation $v = R\omega$ holds, where $R$ is the radius of the cylinder. Therefore, $\omega = \frac{v}{R}$.

Question 48

Which type of motion is characterized by all parts of a rigid body having the same angular velocity at any instant of time?

Accepted Answer

Correct Option: B. Solution: Pure rotation about a fixed axis is characterized by all parts of the body having the same angular velocity at any instant of time.

Question 49

Consider a rigid body in pure rotational motion about a fixed axis. If the angular velocity vector $\omega$ is along the $z$-axis, what is the direction of the linear velocity $v$ of a particle located at a distance $r$ from the axis?

Accepted Answer

Correct Option: C. Solution: The linear velocity $v$ of a particle in rotational motion is given by the vector product $\omega 	imes r$. Thus, $v$ is perpendicular to both the angular velocity vector $\omega$ and the radius vector $r$.

Question 50

A disc of mass $M$ and radius $R$ is rotating about an axis perpendicular to its plane and passing through its center. If the axis is shifted to a point on its edge, what is the new moment of inertia?

Accepted Answer

Correct Option: B. Solution: Using the parallel-axis theorem, the new moment of inertia is $I = I_{cm} + Md^2 = \frac{1}{2}MR^2 + MR^2 = \frac{3}{2}MR^2$.

Question 51

A projectile explodes into two fragments of unequal masses in mid-air. Which of the following statements about the motion of the center of mass of the fragments is correct?

Accepted Answer

Correct Option: B. Solution: The center of mass of the fragments continues along the same parabolic path which it would have followed if there were no explosion, as the external forces remain unchanged.

Question 52

Which of the following statements is true about the angular momentum of a particle relative to a point?

Accepted Answer

Correct Option: B. Solution: Angular momentum is a vector quantity and is conserved if no external torque acts on the system, as per the law of conservation of angular momentum.

Question 53

A cylinder rolls down an inclined plane without slipping. If the plane makes an angle $	heta$ with the horizontal, what is the acceleration of the center of mass of the cylinder?

Accepted Answer

Correct Option: A. Solution: For a rolling object, the acceleration of the center of mass is $a = \frac{g\sin	heta}{1 + \frac{I}{mR^2}}$. For a solid cylinder, $I = \frac{1}{2}mR^2$, so $a = \frac{g\sin	heta}{1 + \frac{1}{2}} = \frac{2}{3}g\sin	heta$.

Question 54

In the context of rotational motion, what is the definition of angular acceleration $\alpha$?

Accepted Answer

Correct Option: A. Solution: Angular acceleration $\alpha$ is defined as the time rate of change of angular velocity.

Question 55

A cylinder of mass $m$ and radius $R$ is rolling without slipping on a horizontal surface with a velocity $v$. What is the total kinetic energy of the cylinder?

Accepted Answer

Correct Option: D. Solution: The total kinetic energy of a rolling object is the sum of its translational and rotational kinetic energies. For a cylinder, $K = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$. Since $I = \frac{1}{2}mR^2$ and $\omega = \frac{v}{R}$, we have $K = \frac{1}{2}mv^2 + \frac{1}{4}mv^2 = \frac{3}{4}mv^2 + \frac{3}{4}mv^2 = \frac{3}{2}mv^2$.

Question 56

A particle of mass $m$ is moving with velocity $\mathbf{v}$ at a position $\mathbf{r}$ from the origin. What is the expression for its angular momentum $\mathbf{L}$ with respect to the origin?

Accepted Answer

Correct Option: B. Solution: The angular momentum $\mathbf{L}$ of a particle with respect to a point is given by $\mathbf{L} = \mathbf{r} 	imes m \mathbf{v}$, where $\mathbf{r}$ is the position vector and $\mathbf{v}$ is the velocity vector.

Question 57

If a torque $	au$ is applied to a rigid body, causing it to rotate about a fixed axis, what is the relationship between the torque and the angular acceleration $\alpha$?

Accepted Answer

Correct Option: A. Solution: The relationship between torque $	au$ and angular acceleration $\alpha$ for a rigid body rotating about a fixed axis is given by $	au = I \alpha$, where $I$ is the moment of inertia of the body.

Question 58

A projectile is launched with an initial velocity and follows a parabolic trajectory. Midway in its path, it explodes into two fragments of equal mass. Assuming no external forces other than gravity act on the system, what will be the path of the center of mass of the fragments?

Accepted Answer

Correct Option: A. Solution: The center of mass of the fragments will continue along the original parabolic path since the explosion is an internal force, and the external force (gravity) remains unchanged.

Question 59

A particle is moving in a circle of radius $r$ with constant speed $v$. What is the angular velocity $\omega$ of the particle?

Accepted Answer

Correct Option: A. Solution: The angular velocity $\omega$ is given by $\omega = \frac{v}{r}$, where $v$ is the linear speed and $r$ is the radius of the circle.

Question 60

What is the equation that describes the motion of the center of mass of a system of particles under external forces?

Accepted Answer

Correct Option: A. Solution: The motion of the center of mass of a system of particles is described by the equation $MA = F_{	ext{ext}}$, where $M$ is the total mass of the system, $A$ is the acceleration of the center of mass, and $F_{	ext{ext}}$ is the sum of all external forces acting on the system.

Question 61

What is the relation between linear velocity $v$ and angular velocity $\omega$ for a particle moving in a circle of radius $r$?

Accepted Answer

Correct Option: A. Solution: The linear velocity $v$ of a particle moving in a circle is related to the angular velocity $\omega$ by the equation $v = \omega r$, where $r$ is the radius of the circle.

Question 62

A thin rod of length $L$ and mass $M$ is rotated about an axis perpendicular to its length and passing through its center. If the moment of inertia of the rod about this axis is $I$, what will be the moment of inertia if the axis is shifted to one of its ends?

Accepted Answer

Correct Option: C. Solution: Using the parallel-axis theorem, the moment of inertia about an axis through one end is $I + \frac{ML^2}{2}$.

Question 63

A rigid body is rotating about a fixed axis with an angular velocity $\omega$. If the angular velocity vector $\omega$ is reversed, what happens to the direction of the linear velocity of a point on the body?

Accepted Answer

Correct Option: B. Solution: Reversing the angular velocity $\omega$ reverses the direction of the linear velocity vector $v = \omega 	imes r$, as the cross product depends on the direction of $\omega$.

Question 64

In an isolated system of particles, what happens to the total linear momentum when no external forces are acting on the system?

Accepted Answer

Correct Option: A. Solution: The law of conservation of linear momentum states that in an isolated system, the total linear momentum remains constant when no external forces are acting on the system.

System of Particles and R..

Learning Objectives

Learning Objectives

Revision Notes & Summary

Chapter Notes

Centre of Mass

Angular Momentum

Torque and Angular Momentum Relation

Vector Product of Two Vectors

Rotational Motion Kinematics

Equilibrium of Rigid Bodies

Conservation of Linear Momentum

Types of Motion of Rigid Bodies

Motion of Centre of Mass

Moment of Inertia

Theorems of Moment of Inertia

Dynamics of Rotation About Fixed Axis

Rolling Motion and Combined Rotation-Translation

Exam Tips & Common Mistakes

Common Mistakes & Exam Tips

Centre of Mass

Angular Momentum

Torque and Angular Momentum Relation

Vector Product of Two Vectors

Rotational Motion Kinematics

Equilibrium of Rigid Bodies

Conservation of Linear Momentum

Types of Motion of Rigid Bodies

Motion of Centre of Mass

Moment of Inertia

Theorems of Moment of Inertia

Dynamics of Rotation About Fixed Axis

Rolling Motion and Combined Rotation-Translation

AI Learning Assistant

Practice Test – MCQs, True/False

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Multiple Choice Questions

Q1.A rigid body is rotating about a fixed axis with an angular velocity ω\omegaω. If a point on the body at a distance rrr from the axis has a linear velocity vvv, what is the relation between vvv, ω\omegaω, and rrr?

Correct Answer: A

Q2.Consider a system of two particles with masses m1m_1m1​ and m2m_2m2​ connected by a light rod of length LLL. If an external torque is applied perpendicular to the rod, what happens to the angular momentum of the system?

Correct Answer: B

Q3.Which of the following statements about the moment of inertia is correct?

Correct Answer: A

Q4.What is the angular momentum lll of a particle with mass mmm, linear momentum ppp, and position vector rrr relative to the origin?

Correct Answer: A

Q5.If a torque τ\tauτ is applied to a rigid body, which of the following statements correctly describes its effect?

Correct Answer: B

Q6.In the context of rotational motion, which of the following correctly describes the relationship between torque τ\tauτ and angular momentum LLL for a single particle?

Correct Answer: A

Q7.A rigid body is rotating about a fixed axis. Which of the following statements is true about the angular velocity vector ω\omegaω?

Correct Answer: C

Q8.A rigid body is subjected to two forces, F1\mathbf{F_1}F1​ and F2\mathbf{F_2}F2​, which are equal in magnitude but opposite in direction and not collinear. What is the effect of these forces on the rigid body?

Correct Answer: B

Q9.Consider a rigid body in equilibrium under the action of several forces. If the net torque about a point on the body is zero, what can be inferred about the forces?

Correct Answer: C

Q10.Consider a particle moving in a circle with radius rrr and angular velocity ω\omegaω. What is the direction of its angular momentum vector?

Correct Answer: B

Q11.A rigid body is in equilibrium under the action of several forces. Which of the following conditions must be satisfied for this equilibrium?

Correct Answer: C

Q12.In the context of rolling motion without slipping, which of the following equations correctly relates linear velocity vvv and angular velocity ω\omegaω?

Correct Answer: A

Q13.A wheel is rotating about a fixed axis with an angular velocity ω\omegaω. If the radius of the wheel is rrr, what is the linear velocity vvv of a point on the rim of the wheel?

Correct Answer: A

Q14.A particle of mass mmm is moving with a constant velocity v\mathbf{v}v. What is the angular momentum of the particle about a point located at a distance rrr from the line of motion of the particle?

Correct Answer: B

Q15.Which of the following conditions must be satisfied for a rigid body to be in mechanical equilibrium?

Correct Answer: B

Q16.For a rigid body in rotational equilibrium, which of the following conditions must be satisfied?

Correct Answer: C

Q17.What is the relationship between torque (τ\tauτ) and angular momentum (LLL) for a single particle?

Correct Answer: A

Q18.Consider a uniform L-shaped lamina composed of two identical square plates each of side aaa. The moment of inertia about an axis passing through the center of mass of the lamina and perpendicular to its plane is given by:

Correct Answer: A

Q19.What is the mathematical expression for the center of mass XXX of a two-particle system with masses m1m_1m1​ and m2m_2m2​ located at positions x1x_1x1​ and x2x_2x2​ respectively?

Correct Answer: A

Q20.A particle is moving in a circular path of radius rrr with a constant speed vvv. If the mass of the particle is mmm, what is the magnitude of its angular momentum about the center of the circle?

Correct Answer: A

Q21.What is the torque τ\tauτ acting on a particle of mass mmm at position vector r\mathbf{r}r due to a force F\mathbf{F}F?

Correct Answer: A

Q22.Consider two vectors a=3i^−4j^+5k^\mathbf{a} = 3\hat{i} - 4\hat{j} + 5\hat{k}a=3i^−4j^​+5k^ and b=−2i^+j^−3k^\mathbf{b} = -2\hat{i} + \hat{j} - 3\hat{k}b=−2i^+j^​−3k^. What is the vector product a×b\mathbf{a} \times \mathbf{b}a×b?