Question

A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is: (Given initial temperature of the bullet = 127°C), Melting point of the bullet = 327°C, Latent heat of fusion of lead = $2.5 × 10^4 J kg^{–1}$ Specific heat capacity of lead = 125 J/kg K)

• A. $125\;ms^{–1}$
• B. $500\;ms^{–1}$
• C. $250\;ms^{–1}$
• D. $600\;ms^{–1}$

Answer 1

Answer: (B)

$500\;ms^{–1}$

Answer 2

The initial speed of bullet is:

$\frac{2}{5}×\frac{1}{2}mv^2=mL+msΔT$

$⇒\frac{v^2}{5}=2.5×10 ^4+125+200$

$⇒\frac{v^2}{5}=5×10^4$

$⇒ v = 500 \;m/s$