NEET Physics: the radius of gyration Practice Questions
9 free multiple-choice questions on the radius of gyration (Rotational Motion) for NEET Physics, each with the correct answer and a step-by-step explanation. Attempt a question, then reveal the solution to check your reasoning.
Practice thousands more NEET questions in the app →Q1. The radius of gyration (k) of a body is defined in terms of its moment of inertia (I) and total mass (M) by the relation:
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Correct answer: B — I = Mk²
The fundamental definition relating the moment of inertia (I), mass (M), and the radius of gyration (k) is I = Mk².
Q2. The relationship between the moment of inertia (I) of a body and its radius of gyration (k) is given by the formula:
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Correct answer: D — I = mk²
The moment of inertia (I) of a body about an axis is related to its total mass (m) and the square of the radius of gyration (k) by the equation I = mk².
Q3. If the mass of a body is doubled while keeping its moment of inertia constant, how does the radius of gyration change?
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Correct answer: A — It is halved
We know I = M k². If I is constant, then M k² = constant. If M is doubled (M' = 2M), then (2M) k² = M k². This implies k² must be halved, so k is halved.
Q4. Which of the following statements correctly defines the radius of gyration (k)?
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Correct answer: B — The distance from the center of mass to the centroid of the mass distribution.
The radius of gyration (k) is defined as the distance from the center of mass of the body to the centroid of the mass distribution.
Q5. For a uniform rod of mass M and length L, the radius of gyration is defined as the distance from the center of mass to which the entire mass is concentrated. What is the value of k for this specific geometry?
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Correct answer: D — L/√12
For a uniform rod of mass M and length L, the moment of inertia about the center is I = ML²/12. Since I = M k², we have M k² = ML²/12, so k² = L²/12, which gives k = L/√12.
Q6. For two objects of the same mass, if the moment of inertia of the first object is greater than the moment of inertia of the second object, which object has the larger radius of gyration?
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Correct answer: D — The first object
Since I = Mk², and M is the same for both, a larger moment of inertia (I) necessarily implies a larger value for k², and thus a larger radius of gyration (k).
Q7. If the mass of a body remains constant, and its radius of gyration (k) is halved, how does its moment of inertia (I) change?
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Correct answer: A — It is quartered
Since I = Mk², if M is constant and k is halved (k' = k/2), then I' = M(k/2)² = M(k²/4) = I/4. Thus, the moment of inertia is quartered.
Q8. For a point mass of mass m rotating at a distance r from the axis, what is the radius of gyration (k)?
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Correct answer: D — k = r
For a point mass, the moment of inertia is I = mr². Since I = Mk², we have mr² = Mk², which simplifies to k² = r², or k=r.
Q9. The radius of gyration is proportional to which of the following quantities?
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Correct answer: D — The moment of inertia of the body
Since k² = I/M, the radius of gyration (k) is proportional to the square root of the moment of inertia divided by the total mass, or directly proportional to √(I/M).
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