A lead bullet at $100^{o} C$ strikes a block of wood, gets embedded in it and melts. Find the speed of the bullet if 50% of the heat produced is shared by the bullet. Specific heat of lead $= 0.03 c a l / g^{o} C$ , latent heat of lead $= 5 c a l / g$ and melting point of lead $= 327^{o} C$ .

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Solution

Heat supplied to the bullet = Q = $\frac{1}{2} \times \frac{1}{2} m v^{2} = \frac{1}{4} m v^{2}$
Heat energy utilised by lead bullet = $m c △ T + m L$ = Q
Equating Q and Q'
$\frac{1}{4} m v^{2}$ = $m c △ T + m L$
$\frac{1}{4} v^{2}$ = $c △ T + L$
Substituting the values,
c= 0.03, L= 5, $△ T$ = 327-100 = 227
v= 6.87 cm/s

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