Two identical masses are connected to a horizontal thin massless rod as shown in the figure. When their distance from the pivot is `x`, a torque produces an angular acceleration `alpha_(1)`. If the masses are now repositioned so that they are at distance `2x` each from the pivot, the same torque will produce an angular acceleration `alpha_(2)` such that ,

Options

A. `alpha_(2)=4alpha_(1)`
B. `alpha_(2)=alpha_(1)`
C. `alpha_(2)=(alpha_(1))/2`
D. `alpha_(2)=(alpha_(1))/4`

Answer

D

Explanation

`tau=(2mx^2)alpha_(1)`
`=(2xxmxx4x^(2))alpha_(2)`
Equating `8mx^(2)alpha_(1)` or `alpha_(2)=(alpha_(1))/4`