The rotating systems shown in the figure differ only in that the two identical movable blocks are positioned a distance r from the axis of rotation (left),or a distance r/2 from the axis of rotation (right).If you release the hanging blocks simultaneously from rest,
A)the block at the left lands first.
B)the block at the right lands first.
C)both blocks land at the same time.

Question

The rotating systems shown in the figure differ only in that the two identical movable blocks are positioned a distance r from the axis of rotation (left),or a distance r/2 from the axis of rotation (right).If you release the hanging blocks simultaneously from rest, 
A)the block at the left lands first. 
B)the block at the right lands first. 
C)both blocks land at the same time.

Quizplus · Accepted Answer

The time period of oscillation for a pendulum is given by T = 2π√(l/g), where l is the length of the pendulum and g is the acceleration due to gravity. In the left case, the length of the pendulum is r, while in the right case, it is r/2. Since the length of the pendulum affects the time period, the right block will oscillate with a shorter time period than the left block. This means that the right block will reach the bottom of its swing before the left block, so answer choice B is correct.

The Rotating Systems Shown in the Figure Differ Only in That