Q: A lead bullet penetrates into a solid object and melts. Assuming that 50% of its kinetic energy was used to heat it, the initial speed of the bullet is (the initial temperature of the bullet is 27 °C and its melting point is 327 °C). Latent heat of fusion of lead = 2.5 × 10^{4} J/kg and specific heat capacity of lead = 125 J/kg-K

(a) 100 m/s

(b) 500 m/s

(c) 800 m/s

(d) 1000 m/s

Ans: (b)

Sol: $\large \frac{1}{2} \times \frac{1}{2}m v^2 = m s \Delta T + m L $

$\large \frac{v^2}{4} = 125 \times (327 – 27) + 2.5 \times 10^4 $

v = 500 m/s