Question

A lead bullet flying with a velocity of $100\,ms^{- 1}$ pierces a fixed board after which its velocity becomes $60\,ms^{- 1}.$ If $40\%$ of energy lost to increases the temperature of bullet, specific heat capacity of lead $=125\,J\,kg^{- 1}K^{- 1}.$ Find change in its temperature (in $\_{}^{^\circ }C$ ). (Approximate the answer to nearest integer)

Answer 1

$v_{b}=200\,ms^{- 1}$
$\Delta K_{\text {loss }}=-\frac{1}{2} m \left(v_{f}^{2}-v_{i}^{2}\right)=-\frac{1}{2} m \left(60^{2}-100^{2}\right)$
$ms\Delta T=0.4\times \frac{1}{2}m\left(\right.160\times 40\left.\right)$
$\Delta T=\frac{0 . 2}{125}\times 160\times 40$
$\Delta T=10.2^\circ C$