A) \[\frac{m}{\sqrt{3}}\]
B) \[\frac{m}{2}\]
C) \[2m\]
D) \[m\]
Correct Answer: D
Solution :
[d] Apply principle of conservation of momentum along x-direction, |
\[mu=m{{v}_{1}}\cos 45+M{{v}_{2}}\cos 45\] |
\[mu=\frac{1}{\sqrt{2}}(m{{v}_{1}}+M{{v}_{2}})\]...(1) |
Along \[y-direction,\] |
\[o=m{{v}_{1}}\sin 45-M{{v}_{2}}\sin 45\] |
\[o=(m{{v}_{1}}-M{{v}_{2}})\frac{1}{\sqrt{2}}.....(2)\] |
Coefficient of \[e=1=\frac{{{v}_{2}}-{{v}_{1}}\cos 90}{u\cos 45}\] |
Restution |
\[\Rightarrow \frac{{{v}_{2}}}{\frac{u}{\sqrt{2}}}=1\] |
\[\Rightarrow u=\sqrt{2}{{v}_{2}}.....(3)\] |
Solving eqn. (1), (2), & (3) we get |
\[M=m\] |
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