Q98 / 120 · VITEEE 2013 · Physics
A body of mass $2 \mathrm{~kg}$ moving with velocity of $6 \mathrm{~m} / \mathrm{s}$ strikes in elastically with another body of same mass mass at rest. The amount of heat evolved during collision is
- Correct answerA$18 \mathrm{~J}$
- B$36 \mathrm{~J}$
- C$9 \mathrm{~J}$
- D$3 \mathrm{~J}$
Solution
Common velocity, $\mathrm{v}=\frac{\mathrm{m}_{1} \mathrm{v}_{1}+\mathrm{m}_{2} \mathrm{v}_{2}}{\mathrm{~m}_{1}+\mathrm{m}_{2}}$
$\begin{array}{l}
=\frac{2 \times 6+2 \times 0}{2+2}=3 \mathrm{~m} / \mathrm{s} \\
\text { Initial kinetic energy }\left(\mathrm{E}_{1}\right) \\
=\frac{1}{2} \mathrm{~m}_{1} \mathrm{v}_{1}^{2}+\frac{1}{2} \mathrm{~m}_{2} \mathrm{v}_{2}^{2}=\frac{1}{2} \times 2 \times(6)^{2}=36 \mathrm{~J} \\
=\frac{1}{2}\left(\mathrm{~m}_{1}+\mathrm{m}_{2}\right) \mathrm{V}^{2}=\frac{1}{2}(2+2)(3)^{2}=18 \mathrm{~J} \\
\therefore \text { Heat evolved }=(36-18) \mathrm{J}=18 \mathrm{~J}
\end{array}$
Hence, the correct answer is option: 'A'.