Question

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 ${25}^{o}C$ and its melting point is ${300}^{o}C$). Latent heat of fusion of lead $=2.5\times {10}^{4}J/kg$ and specific heat capacity of lead $=125J/kg-K$.

• A. $100m/s$
• B. $\simeq 490m/s$
• C. $520m/s$
• D. $360m/s$

Answer 1

The correct option is B $\simeq 490m/s$

Given, $S=125J/kg-K$
$\theta ={25}^{o}C$, $\theta ={300}^{o}C$, $m=2.5\times {10}^{4}J/kg$, then
$\frac{1}{2}m{v}^2\times \frac{1}{2}=mS\Delta \theta +mL$
$\Rightarrow \frac{v^2}{4}=125(300-25)+2.5\times {10}^4$
$\Rightarrow \frac{v^2}{4}=59375$
$\Rightarrow v^2=59375\times 4$
$\Rightarrow v=\sqrt{237500}\Rightarrow v=487.3m/s$
$\Rightarrow v=490m/s$