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

The Correct Option is A

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 $