Rotational Motion
Q. Which of the following has the smallest moment of inertia about an axis through its center?
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A.
Solid cylinder
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B.
Hollow cylinder
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C.
Solid sphere
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D.
Hollow sphere
Solution
The solid sphere has the smallest moment of inertia compared to the other shapes for the same mass and radius.
Correct Answer: C — Solid sphere
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Q. Which of the following quantities is conserved in a closed system of rotating bodies?
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A.
Linear momentum
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B.
Angular momentum
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C.
Kinetic energy
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D.
All of the above
Solution
In a closed system, angular momentum is conserved, while linear momentum and kinetic energy may not be.
Correct Answer: B — Angular momentum
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Q. Which of the following quantities is conserved in a closed system with no external torques acting on it?
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A.
Angular momentum
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B.
Linear momentum
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C.
Energy
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D.
All of the above
Solution
In a closed system with no external torques, angular momentum is conserved.
Correct Answer: A — Angular momentum
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Q. Which of the following quantities is conserved in a closed system with no external torques?
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A.
Linear momentum
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B.
Angular momentum
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C.
Energy
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D.
All of the above
Solution
In a closed system with no external torques, angular momentum is conserved.
Correct Answer: B — Angular momentum
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Q. Which of the following quantities is conserved in an isolated system when no external torques act?
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A.
Linear momentum
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B.
Angular momentum
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C.
Both linear and angular momentum
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D.
Neither
Solution
In an isolated system with no external torques, angular momentum is conserved.
Correct Answer: B — Angular momentum
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Q. Which of the following quantities is conserved in the absence of external torques?
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A.
Linear momentum
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B.
Angular momentum
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C.
Energy
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D.
All of the above
Solution
In the absence of external torques, angular momentum is conserved.
Correct Answer: B — Angular momentum
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Q. Which of the following shapes has the largest moment of inertia for the same mass and radius?
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A.
Solid sphere
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B.
Hollow sphere
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C.
Solid cylinder
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D.
Hollow cylinder
Solution
The hollow sphere has the largest moment of inertia compared to the other shapes for the same mass and radius.
Correct Answer: B — Hollow sphere
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Q. Which of the following statements about torque is true?
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A.
Torque is a scalar quantity.
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B.
Torque depends on the angle of application.
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C.
Torque is always positive.
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D.
Torque does not depend on the point of rotation.
Solution
Torque depends on the angle of application, as it is calculated using τ = F × d × sin(θ).
Correct Answer: B — Torque depends on the angle of application.
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Q. Which of the following statements is true regarding the moment of inertia?
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A.
It depends on the mass distribution
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B.
It is always constant
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C.
It is independent of the axis of rotation
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D.
It is only relevant for rigid bodies
Solution
The moment of inertia depends on the mass distribution relative to the axis of rotation.
Correct Answer: A — It depends on the mass distribution
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Q. Which theorem is used to find the moment of inertia of a body about an axis that is parallel to an axis through its center of mass?
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A.
Perpendicular axis theorem
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B.
Parallel axis theorem
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C.
Pythagorean theorem
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D.
Conservation of angular momentum
Solution
The parallel axis theorem is used to find the moment of inertia about an axis parallel to one through the center of mass.
Correct Answer: B — Parallel axis theorem
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