A) \[m\]
B) \[2\,\,m\]
C) \[3\,\,m\]
D) \[\frac{3}{2}m\]
Correct Answer: C
Solution :
Key Idea: In elastic collision kinetic energy and momentum are conserved. Let \[{{u}_{1}}\] be the initial velocity of a particle before collision and \[{{v}_{1}}\] the final velocity after collision, then change in kinetic energy is given by \[\frac{1}{2}{{m}_{1}}u_{1}^{2}-\frac{1}{2}{{m}_{1}}v_{1}^{2}=\frac{75}{100}\times \frac{1}{2}{{m}_{1}}v_{1}^{2}\] \[\Rightarrow \] \[u_{1}^{2}-v_{1}^{2}=\frac{3}{4}u_{1}^{2}\] \[\Rightarrow \] \[{{v}_{1}}=\frac{1}{1}{{u}_{1}}\] Also from conservation of momentum, we have \[{{v}_{1}}=\frac{({{m}_{2}}-{{m}_{1}}){{u}_{1}}}{({{m}_{1}}+{{m}_{2}})}\] Thus, \[\frac{1}{2}{{u}_{1}}=\frac{({{m}_{2}}-{{m}_{1}}){{u}_{1}}}{{{m}_{1}}+{{m}_{2}}}\] \[\Rightarrow \] \[{{m}_{2}}=3{{m}_{1}}=3m\]You need to login to perform this action.
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