Question

A lead bullet moving with velocity '\(v\)' strikes a wall and stops. \(75\%\) of its energy is converted into heat. If the increase in the temperature is \(\frac{v^{2}}{nJs}\), then the value of \(n\) is \(\{s=\text{specific heat of lead},J=\text{mechanical equivalent of heat}\}\)

• A. \(\frac{8}{3}\)
• B. \(\frac{4}{3}\)
• C. \(\frac{3}{8}\)
• D. \(\frac{3}{4}\)

Hint:

Equate 75 percent of the kinetic energy to the heat gained, converting calories to joules with the mechanical equivalent J.

Answer 1

The Correct Option is A

Step 1: Kinetic energy used
Energy converted to heat $=\frac{75}{100}\times\frac{1}{2}mv^{2}=\frac{3mv^{2}}{8}$.

Step 2: Heat relation
Work equivalent of the heat gained is $J\,ms\Delta T$, so $\Delta T=\frac{3v^{2}}{8Js}$.

Step 3: Match
$\frac{3}{8}=\frac{1}{n}$, so $n=\frac{8}{3}$, matching option (A).

Final Answer:
The required value is $n=\frac{8}{3}$. \[ \boxed{\text{(A) }\dfrac{8}{3}} \]