A thin circular metal disc of radius 500.0 mm is set rotating about a central axis normal to its plane. Upon raising its temperature gradually, the radius increases to 507.5 mm. The percentage change in the rotational kinetic energy will be

Options

A. `1.5%`
B. `-1.5%`
C. `3%`
D. `-3%`

Answer

D

Explanation

Given, `(dR)/(R)xx100=((507.5-500.0))/(500.0)xx100=1.5%`
Now `K=(1)/(2)Iomega^2=(1)/(2I)(Iomega)^2=(L^2)/(2I)`
or `K=(L^2)/(2((MR^2)/(2)))=(L^2)/(R)(R^-2)`
Taking log and differentiating, `(dK)/(K)=-(2dR)/(R)`
or `%` change in `K=(dKxx100)/(K)=-(2dR)/(R)xx100=-3%`