The angular retardation of a rotating flywheel is proportional to the angle through which it rotates. If its kinetic energy gets reduced by `Delta E` while it rotates through at an angle `theta`, then

Options

A. `Delta Eprop theta^(2)`
B. `Delta Eprop sqrt(theta)`
C. `Delta E prop theta`
D. `Delta E prop theta^((3)/(2))`

Answer

A

Explanation

We known that the given body is performing angular SHM ,
`KE = (1)/(2) k(A^(2)-x^(2))`
`rArr KE = (1)/(2) k (theta_(0)^(2) - theta^(2))`
Hence, reduced kinectic energy `Delta E` is
or `Delta E prop theta^(2)`