A) 4.09 kg
B) 0.5 kg
C) 5 kg
D) 5.09 kg
Correct Answer: A
Solution :
For elastic collision, \[e=1\] Given that, \[\text{Ist}\]body moves and \[\text{IInd}\]body is at rest After 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 Eq. (i), we get \[\frac{9}{2}u=M\left( \frac{11u}{10} \right)\] or \[\frac{5\times 9}{11}=M\] or \[M=\frac{45}{11}=4.09\,kg\]You need to login to perform this action.
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