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

KE of rotating = Heat energy
`(1)/(2)I omega^(2)=MSd theta`
`(75)/(100)xx(1)/(2)xx(2)/(3)MR^(2)omega^(2) = MSd theta`
`therefore " " d theta = (2)/(3)xx(1)/(2)(R^(2)omega^(2))/(S)xx(75)/(100)`
`= (R^(2)omega^(2))/(4 S)`