A ball moving with speed v hits another identical ball at rest. The two balls stick together after collision. If specific heat of the material of the balls is S , the temperature rise resulting from the collision is

Options

A. ` ( v^(2))/( 8s) `
B. ` ( v^(2))/( 4S ) `
C. ` ( v^(2))/( 2S) `
D. ` (v^(2))/( S) `

Answer

A

Explanation

Initial momentum =mv
Finanl momentum = 2mv
K.E. Of the system after the collision `= (1)/(2) (2m ) ((v)/(2)) ^(2) `
` therefore ` loss in K.E. `(1)/(2) mv ^(2) - (1)/(4) mv^(2) = (1)/(4) mv^(2) `
This loss in K.E. will increase the temperature
` therefore 2m xx s xx Delta t = (1)/(4) mv^(2) rArr Delta t = ( v^(2))/( 8s) `