| A ball of mass m, moving with a speed of \[2{{v}_{0}}\] collides in elastically with an identical ball at rest. |
 |
| Now, choose the correct option. |
A) For a general head on collision first ball retraces its path backwards
B) For a general head on collision first ball stops after collision
C) For a general head on collision angle between velocities of scattered balls is \[90{}^\circ \]
D) For a general head on collision angle between velocities of scattered balls is less than \[90{}^\circ \]
Correct Answer: D
Solution :
| By conservation of momentum, |
| \[{{p}_{i}}={{p}_{1}}+{{p}_{2}}\] |
| For a general collision, some energy is lost |
| \[\Rightarrow \]\[\frac{p_{i}^{2}}{2m}>\frac{p_{1}^{2}}{2m}+\frac{p_{2}^{2}}{2m}\]\[\Rightarrow \]\[{{p}^{2}}>p_{1}^{2}+p_{2}^{2}\] |
| \[\therefore \] \[\theta <90{}^\circ \] |
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