Question

A body of mass 5 kg makes an elastic collision with another body at rest and continues to move in the original direction after collision with a velocity equal to $\frac{1}{10}$ th of its original velocity. Then the mass of the second body is

• A. 4.09 kg
• B. 0.5 kg
• C. 5 kg
• D. 5.09 kg

Answer 1

Answer: (A)

4.09 kg

Answer 2

For elastic collision, $e=1$ Given that, $\text{Ist}$ body moves and $\text{IInd}$ body is at restAfter collision velocity of 5 kg mass becomes $\frac{u}{10}.$ By law of conservation of momentum, ${{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}={{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}$ $\therefore$ $5\times u+M\times 0=5\times \frac{u}{10}+M{{v}_{2}}$ or $5u-\frac{u}{2}=M{{v}_{2}}$ or $\frac{9u}{2}=M{{v}_{2}}$ ?(i) Also . ${{v}_{1}}-{{v}_{2}}=-e({{u}_{1}}-{{u}_{2}})$ But e = 1 (e = coefficient of restitution) $\therefore$ $\frac{u}{10}-{{v}_{2}}=-(u)$ or $\frac{u}{10}+u={{v}_{2}}$ or $\frac{11u}{10}={{v}_{2}}$ ?(ii) Substituting the value of ${{v}_{2}}$ in E (i), we get $\frac{9}{2}u=M\left( \frac{11u}{10} \right)$ or $\frac{5\times 9}{11}=M$ or $M=\frac{45}{11}=4.09\,kg$