A hollow spere of mass M and radius R is rotating with angular frequency `omega` it suddenly stops rotating and 75% of kinetic energy is converted to heat if s is the speicific heat of the material in j / kg k then rise in temperature of the spere is (MI of hollow sphere `=2/3MR^(2)`

Options

A. `(R omega)/(4s)`
B. `(R^(2)omega^(2))/(4s)`
C. `(R omega)/(2s)`
D. `(R^(2)omega^(2))/(2s)`

Answer

b

Explanation

Intial rotational kinetic energy of the hollow sphere
`k_(i)=1/2xxIomega^(2)=1/2 xx2/3mr^(2)xx(v^(2))/(r^(2))`
`=1/3 mv^(2)=1/3m xx omega^(2)R^(2)`
according to the question
`rarr 3/4xx1/3 omega^(2)R^(2)=S Delta theta`
`therefore` Rise in temperature of the sphere
`Delta theat =1/4 (omega^(2)R^(2))/(S)`