| A: In a one-dimensional perfectly elastic collision between two moving bodies of equal masses the bodies merely exchange their velocities after collision. |
| B: If a lighter body at rest suffers perfectly elastic collision with a very heavy body moving with a certain velocity after collision both travel with same velocity. |
A) A and B are correct
B) both A and B are wrong
C) A is correct, B is wrong
D) A is wrong, B is correct
Correct Answer: C
Solution :
Velocities after collision are\[{{v}_{1}}=\left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right){{\mu }_{1}}+\left( \frac{2{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right){{\mu }_{2}}\]and \[{{v}_{2}}=\left( \frac{2{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}} \right){{\mu }_{1}}+\left( \frac{{{m}_{2}}-{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}} \right){{\mu }_{2}}\]When the two colliding particles have equal masses i.e., \[{{m}_{1}}={{m}_{2}}\] Now, putting the value \[{{m}_{1}}={{m}_{2}}\]in above equation, \[{{v}_{1}}={{u}_{2}}\]and \[{{v}_{2}}={{u}_{1}}\] Thus, in one dimensional elastic collision the particles simply exchange velocities during collision. Hence, statement is correct. In case B, when\[{{m}_{2}}<<{{m}_{1}}\] that is in the collision of heavy particle with a light particle at rest, the velocity of heavy particle remains unchanged. While light particle runs with nearly twice the velocity of the incident particle. Hence, case B is not true.
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