This question has statement I and Statement II. Of the four choice given after the statements, choose the one that best describes the two statements. |
Statement - I: A Point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as |
\[f\left( \frac{1}{2}m{{v}^{2}} \right)\]then\[f=\left( \frac{m}{M+m} \right)\] |
Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision. [JEE MAIN 2013] |
A) Statement - I is true, Statement - II is true, statement - II is a correct explanation of Statement I
B) Statement - I is true, Statement - II is true, statement - II is not a correct explanation of Statement I
C) Statement - I is true, Statement - II is false
D) Statement - I is false, Statement - II is true
Correct Answer: D
Solution :
[d] Maximum energy loss when inelastic collision takes place |
\[mv=(m+M)v\prime \] |
\[v\prime =\frac{m}{m+M}v\] |
\[{{k}_{i}}=\frac{1}{2}m{{v}^{2}}\] |
\[{{k}_{f}}=\frac{1}{2}(m+M)v{{'}^{2}}=\frac{1}{2}(m+M)\frac{{{m}^{2}}{{v}^{2}}}{{{(m+M)}^{2}}}\] |
\[=\frac{1}{2}m{{v}^{2}}\left( \frac{m}{M+m} \right)\] |
Loss of energy\[={{k}_{i}}-{{k}_{f}}=\frac{1}{2}m{{v}^{2}}\left[ 1-\frac{m}{M+m} \right]\] |
\[=\frac{M}{M+m}\times \frac{1}{2}m{{v}^{2}}\] |
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