A toruque `tau` produces an angular acceleration in a body rotating about an axis of rotation. The moment of inertia of the body is increased by `50%` by redistributing the masses, about the axis of rotation. To maintain the same angular acceleration, the torque is changed to `tau'`. What is the relation between `tau and tau'`?

Options

A. `tau'=tau`
B. `tau'=(2)/(3)tau`
C. `tau'=(3)/(2)tau`
D. `tau'=(tau)/(2)`

Answer

C

Explanation

`"Initially " tau=Ialpha" …(1)"`
In the second case I is increased by `50%`.
`"i.e. I'"=(I+(50)/(100)I)=(3)/(2)I`
`therefore" "tau'=I'alpha=(3)/(2)Ialpha=(3)/(2)tau`