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. `(Romega)/(4S)`
B. `(R^(2)omega^(2))/(4S)`
C. `(Romega)/(2S)`
D. `(R^(2)omega^(2))/(2S)`

Answer

B

Explanation

For the rotating sphere,
`K.E.=(1)/(2)Iomega^(2)=(1)/(2)((2)/(3)MR^(2))omega^(2)=(1)/(3)MR^(2)omega^(2)`
The K.E. converted into heat
`=(3)/(4)((1)/(3)MR^(2)omega^(2))=(1)/(4)MR^(2)omega^(2)" …(1)"`
If `d theta` is the rise in temperature of the sphere, the heat required `=MSd theta" ...(2)"`
`therefore" from (1) and (2), MSd "theta=(1)/(4)MR^(2)omega^(2)`
`therefore d theta=(1)/(4)(R^(2)omega^(2))/(S)`