A metal sphere of radius r and specific heat s is rotated about an axis passing through its centre at a speed of n rotation/s. It is suddenly stopped and `50%` of its energy is used in increasing its temperature. Then, the rise in temperature of the sphere is

Options

A. `(2pi^(2)n^(2)r^(2))/(5s)`
B. `(1pi^(2)n^(2))/(10r^(2)s)`
C. `(7)/(8)pir^(2)n^(2)s`
D. `(5(pirn)^(2))/(14s)`

Answer

A

Explanation

Heat, `DeltaQ = (1)/(2)K>E`
`DeltaQ = (1)/(2)xx(1)/(2)Iomega^(2)` `(because K.E= (1)/(2)Iomega^(2))`
`DeltaQ = (1)/(2)xx(1)/(2)xx(2)/(5)mr^(2)xx(2pin)^(2)`
`mstDeltat = (2)/(5)mr^(2)pi^(2)n^(2)`
`Deltat = (2pi^(2)n^(2)r^(2))/(5S)`