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  4. A body of mass 2 kg moving with a velocity of 6 m/s strikes in elastically another body of same mass at rest. The amount of heat evolved is

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Q. A body of mass 2 kg moving with a velocity of 6 m/s strikes in elastically another body of same mass at rest. The amount of heat evolved is

VMMC MedicalVMMC Medical 2015

Solution:

Common velocity $ =\frac{{{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}}{{{m}_{1}}+{{m}_{2}}} $ $ =\frac{2\times 6+2\times 0}{2+2} $ $ =3m\text{/}s $ Initial kinetic energy $ =\frac{1}{2}{{m}_{1}}v_{1}^{2}+\frac{1}{2}{{m}_{2}}v_{2}^{2} $ $ =\frac{1}{2}\times 2\times {{(6)}^{2}} $ = 36 J Final kinetic energy $ =\frac{1}{2}({{m}_{1}}+{{m}_{2}}){{v}^{2}} $ $ =\frac{1}{2}(2+2){{(3)}^{2}}=18J $ The amount of heat evolved $ ={{E}_{1}}-{{E}_{2}} $ = 36 ? 18 = 18J