Question

A body of mass m strikes another body at rest of mass $\frac{m}{9}$ . Assuming the impact to be inelastic the fraction of the initial kinetic energy transformed into heat during the contact is

• A. 0.1
• B. 0.2
• C. 0.5
• D. 0.64

Answer 1

Answer: (A)

0.1

Answer 2

The loss in kinetic energy which is transformed into heat $=\frac{1}{2}\left( \frac{{{m}_{1}}{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right){{({{u}_{1}}+{{u}_{2}})}^{2}}$ Here, ${{m}_{1}}=m,\,{{m}_{2}}=\frac{m}{9},{{u}_{1}}=u,{{u}_{2}}=0$ Loss $\Delta \Epsilon =\frac{1}{2}\left( \frac{m\times \frac{m}{9}}{m+\frac{m}{9}} \right)\times {{(u+0)}^{2}}=\frac{1}{2}\frac{m}{10}{{u}^{2}}$ Now, initial kinetic energy $=\frac{1}{2}m{{u}^{2}}$ $\text{Required}\,\text{fraction =}\frac{\text{loss}\,\text{in kinetic}\,\text{energy}}{\text{initial}\,\text{kinetic}\,\text{energy}}$ $=\frac{\frac{1}{2}\frac{m}{10}{{u}^{2}}}{\frac{1}{2}m{{u}^{2}}}$ $=\frac{1}{10}=0.1$