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  • Two billiard balls of equal mass strike a rigid wall with same speed of (as shown) but at different ang

Two billiard balls of equal mass 30 \mathrm{~g} strike a rigid wall with same speed of 108 \mathrm{kmph} (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball ' a 'and ball 'b' by the wall along ' X^{\prime} direction is :
Option: 1 1:1      
Option: 2 \sqrt{2}:1
Option: 3 2:1
Option: 4 1:\sqrt{2}

Answers (1)

best_answer

   

For ball a,  
\bar{p_{i}}= m{u} \hat{i}
\bar{p_{f}}= m{u}\left (\hat{-i} \right )
Impulse \, imparted \, to \, ball\, a \rightarrow \Delta \bar{p}_{a}= -2m{u}\left ( \hat{i} \right ) \rightarrow \left ( 1 \right )
For ball b,
\bar{p_{i}}= mu\cos 45^{\circ}\hat{i}+mu\sin 45^{\circ}\left ( -\hat{j} \right )                    
  \bar{p_{f}}= mu\cos 45^{\circ}\left ( -\hat{i} \right )+mu\sin 45^{\circ}\left ( -\hat{j} \right )        
\Delta \bar{p}= 2mu\cos 45^{\circ}\left ( -\hat{i} \right )\rightarrow \left ( 2 \right )   

               
Impulse imported to ball b
1\div 2
\frac{\left | \Delta \bar{p}_{a} \right |}{\left | \Delta \bar{p}_{b} \right |}= \frac{2mu}{2mu\cos 45^{\circ}}= \sqrt{2}
The correct option is (2)

Posted by

vishal kumar

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