Question

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:

• A. $v^2/8S$
• B. $v^2/4S$
• C. $v^2/2S$
• D. $v^2/S$

Answer 1

The correct option is A $v^2/8S$

By conservation of momentum, final velocity$=v/2$

And by energy conservation,

Initial K.E=Final K.E+heat

$\frac{m{v}^2}{2}=\frac{m{v}^2}{4}+2mS\left(\Delta T\right)$

$\Delta T=\frac{v^2}{8S}$