Assertion (A): It will be much easier to accelerate a merry-go-round full of children if they stand close to its axis then if they all stand at the outer edge. Reason (R): For larger moment of inertia, the angular acceleration is small for given torque.
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false
Solution:
From the relation \(tau = I alpha\), where \(tau\) is torque, \(I\) is moment of inertia, and \(alpha\) is angular acceleration. If children stand closer to the axis, \(I\) decreases. For a given \(tau\), a smaller \(I\) leads to a larger \(alpha\), making it easier to accelerate. So, (A) is true. Reason (R) states that for larger \(I\), \(alpha\) is small for given \(tau\), which is also true and explains (A).
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