30 MCQ question based on system of particles and rotational motion with answer and explanation
1. Which of the following quantities is a vector quantity?
a) Angular velocity
b) Angular displacement
c) Angular acceleration
d) Moment of inertia
Answer: a) Angular velocity
Explanation: Angular velocity is a vector quantity because it has both magnitude and direction.
2. The unit of moment of inertia is:
a) Kg/m^2
b) Kgm^2
c) m^2/Kg
d) m^2/s^2
Answer: b) Kgm^2
Explanation: Moment of inertia is the rotational analogue of mass and is measured in Kg*m^2.
3. Which of the following statements is true regarding angular acceleration?
a) It is a scalar quantity
b) It is measured in radians per second
c) It is the rate of change of angular velocity
d) It is given by the formula F=ma
Answer: c) It is the rate of change of angular velocity
Explanation: Angular acceleration is the rate of change of angular velocity and is measured in radians per second squared.
4. Which of the following quantities is a scalar quantity?
a) Angular velocity
b) Angular displacement
c) Torque
d) Moment of inertia
Answer: d) Moment of inertia
Explanation: Moment of inertia is a scalar quantity because it only has magnitude and no direction.
5. The rotational analogue of force is:
a) Torque
b) Moment of inertia
c) Angular velocity
d) Angular displacement
Answer: a) Torque
Explanation: Torque is the rotational analogue of force and is responsible for causing rotational motion.
6. A rigid body is rotating about a fixed axis. Which of the following quantities remains constant?
a) Angular velocity
b) Angular acceleration
c) Moment of inertia
d) None of the above
Answer: c) Moment of inertia
Explanation: In a rigid body rotating about a fixed axis, the moment of inertia remains constant.
7. The direction of torque is given by:
a) The direction of the applied force
b) The direction of the displacement of the object
c) The direction of the axis of rotation
d) The direction perpendicular to the plane containing the applied force and the displacement vector
Answer: d) The direction perpendicular to the plane containing the applied force and the displacement vector
Explanation: The direction of torque is given by the right-hand rule, which states that the direction of torque is perpendicular to the plane containing the applied force and the displacement vector.
8. Which of the following statements is true regarding rotational kinetic energy?
a) It depends on the linear velocity of the object
b) It depends on the mass of the object
c) It depends on the moment of inertia of the object
d) It is independent of the rotational speed of the object
Answer: c) It depends on the moment of inertia of the object
Explanation: Rotational kinetic energy is given by the formula KE = (1/2)Iw^2, where I is the moment of inertia and w is the angular velocity.
9. Which of the following quantities is not conserved in rotational motion?
a) Angular momentum
b) Angular velocity
c) Moment of inertia
d) None of the above
Answer: b) Angular velocity
Explanation: Angular velocity is not conserved in rotational motion because it can change due to the application of torque.
10. The condition for a body to be in translational equilibrium is:
a) The net force acting on the body is zero
b) The net torque acting on the body is zero
c) The net force and the net torque acting on the body are zero
d) None of the above
Answer: a) The net force acting on the body is
11. The rotational inertia of an object depends on:
a) The mass and the radius of the object
b) The mass and the velocity of the object
c) The mass and the shape of the object
d) The mass and the acceleration of the object
Answer: c) The mass and the shape of the object
Explanation: The moment of inertia or rotational inertia of an object depends on the mass distribution and the shape of the object.
12. The angular momentum of a rotating object is given by:
a) L = mv
b) L = Iω
c) L = Fd
d) L = E/t
Answer: b) L = Iω
Explanation: The angular momentum of a rotating object is given by the product of its moment of inertia and angular velocity, i.e. L = Iω.
13. Which of the following statements is true regarding center of mass?
a) It is the point at which the entire mass of an object is concentrated
b) It is always located at the geometric center of an object
c) It can be located outside the physical boundaries of an object
d) It is the same as the axis of rotation of an object
Answer: c) It can be located outside the physical boundaries of an object
Explanation: The center of mass is the point where the entire mass of an object can be assumed to be concentrated, and it can be located outside the physical boundaries of an object if the mass distribution is not uniform.
14. The radius of gyration of an object is:
a) The distance between the center of mass and the axis of rotation
b) The distance from the center of mass to any point on the object
c) The radius of the circular path followed by the object
d) The distance from the axis of rotation to a point where the object has maximum velocity
Answer: a) The distance between the center of mass and the axis of rotation
Explanation: The radius of gyration is a measure of how the mass of an object is distributed about the axis of rotation, and it is defined as the distance from the axis of rotation to a point where the entire mass of the object can be assumed to be concentrated.
15. The moment of inertia of a uniform thin rod of length L and mass M, about an axis perpendicular to the rod passing through its center is:
a) (1/12)ML^2
b) (1/4)ML^2
c) (1/3)ML^2
d) (1/2)ML^2
Answer: c) (1/3)ML^2
Explanation: The moment of inertia of a uniform thin rod of length L and mass M, about an axis perpendicular to the rod passing through its center is given by (1/12)ML^2, but if the axis of rotation is shifted to one end of the rod, the moment of inertia becomes (1/3)ML^2.
16. The moment of inertia of a solid sphere of mass M and radius R about its diameter is:
a) (2/5)MR^2
b) (1/2)MR^2
c) (3/5)MR^2
d) (2/3)MR^2
Answer: a) (2/5)MR^2
Explanation: The moment of inertia of a solid sphere of mass M and radius R about its diameter is (2/5)MR^2.
17. The angular momentum of an isolated system:
a) Remains constant
b) Increases with time
c) Decreases with time
d) Can either increase or decrease
18.A disc of mass M and radius R is rotating about its axis with an angular velocity ω. If the angular velocity is doubled, the kinetic energy of the disc will become:
a) 2K
b) 4K
c) 8K
d) 16K
Answer: d) 16K
Explanation: The kinetic energy of a rotating object is given by K = (1/2)Iω^2, where I is the moment of inertia of the object. Doubling the angular velocity will result in the kinetic energy becoming four times the initial value, so the answer is 16K.
19. Two particles of masses m1 and m2 are attached to the ends of a rigid rod of length L. The moment of inertia of this system about an axis passing through the center of mass perpendicular to the rod is:
a) (m1+m2)L^2/12
b) (m1+m2)L^2/8
c) (m1+m2)L^2/6
d) (m1+m2)L^2/4
Answer: d) (m1+m2)L^2/4
Explanation: The moment of inertia of a system of particles about an axis passing through the center of mass perpendicular to the rod is given by I = Σmiri^2, where ri is the distance of the ith particle from the axis of rotation. For a rod of length L and particles of masses m1 and m2 at the ends, the moment of inertia is (m1+m2)L^2/12 + (m1+m2)L^2/12 = (m1+m2)L^2/6. However, since the axis of rotation passes through the center of mass, the parallel axis theorem can be used to find the moment of inertia about this axis, which is given by I = (m1+m2)L^2/6 + ML^2/12, where M = m1 + m2 is the total mass of the system. Simplifying this expression gives the answer (m1+m2)L^2/4.
20. Which of the following statements is true regarding rotational motion?
a) The direction of angular velocity is always perpendicular to the plane of rotation.
b) The moment of inertia depends on both the mass and the shape of the object.
c) The angular acceleration is directly proportional to the net torque acting on the object.
d) The angular momentum of a system is always conserved.
Answer: b) The moment of inertia depends on both the mass and the shape of the object.
Explanation: Rotational motion is the motion of an object about an axis, and is characterized by several quantities, including angular displacement, angular velocity, angular acceleration, torque, moment of inertia, and angular momentum.
BONUS QUESTIONS
21. What is the moment of inertia of an object?
a) The force required to produce a unit of linear acceleration in the object.
b) The force required to produce a unit of angular acceleration in the object.
c) The resistance of the object to rotational motion.
d) The ability of the object to resist linear motion.
Answer: c) The resistance of the object to rotational motion.
Explanation: The moment of inertia of an object is a measure of the object's resistance to rotational motion about a given axis. It is defined as the sum of the products of each particle's mass and the square of its distance from the axis of rotation. Mathematically, the moment of inertia I is given by the integral I = ∫r^2 dm, where r is the distance from the axis of rotation to each infinitesimal mass element dm.
Option a) is incorrect because it refers to the concept of linear inertia, which is the resistance of an object to changes in its linear motion.
Option b) is also incorrect because it does not accurately define the moment of inertia. The force required to produce a unit of angular acceleration is known as the torque.
Option d) is incorrect because it refers to the concept of linear motion and not rotational motion. The ability of an object to resist linear motion is described by its mass, not its moment of inertia.
I hope that you have enjoyed these questions. Next time i will come with some more informative questions with answer.
----------------------------
Comments
Post a Comment