A metal sphere of radious R and specific heat C is rotated about an axis passing through its centre at a speed n rotation/second. It is suddenly stopped and 50% of its energy is converted in thermal energy, then find the rise in temperature of the sphere.

Options

A. `(pi^(2)n^(2)R^(2))/(5C)`
B. `(2pin^(2)R^(2))/(5C)`
C. `(2pi^(2)n^(2)R^(2))/(5C)`
D. `(pin^(2)R^(2))/(5C)`

Answer

C

Explanation

K.E. of spese `(1)/(2) I omega^(2)`
`(1)/(2) xx (2)/(5) MR^(2) xx 4 pi^(2) n^(2)`
50% of this energy
`rArr (2)/(5) MR^(2) pi^(2) h^(2) = MC DeltaT`
`Delta T = (2)/(5) (R^(2)pi^(2)h^(2))/(C )`