A rigid body is rotating about a vertical axis. In `t` second, the axis gradually becomes horizontal. But the rigid body continues to make `v` rotations per second throughout the time interval of `1` second. If the moment of inertia `I` of the body about the axis of rotation can he taken as constant, then the torque acting on the body is

Options

A. `2piv`I
B. `2sqrt(2)piv`I
C. `(2sqrt2piv)/t`I
D. `(2sqrt(2)pivl)/t`I

Answer

D

Explanation

`vectau=Ivecalpha` or `vectauI=(I(vecomega_(2)-vecomega_(1)))/t`
But `|omega_(2)-vecomega_(1)|=sqrt(omega_(2)^(2)+omega_(1)^(2))=sqrt(2)omega=sqrt(2)xx2piv`
`tau=I/txx2sqrt(2)piv` or `tau=(2sqrt(2)pivI)/t`