JEE MAIN - Physics (2021 - 25th July Morning Shift - No. 11)
Two billiard balls of equal mass 30g strike a rigid wall with same speed of 108 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' direction is :
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1 : 1
$$\sqrt 2 $$ : 1
2 : 1
1 : $$\sqrt 2 $$
Explanation
Impulse = change in momentum
Ball (a) $$\left| {\overrightarrow {\Delta p} } \right|$$ = 2mu = J1
Ball (b) $$\left| {\overrightarrow {\Delta p} } \right|$$ = 2mu cos45$$^\circ$$ = J2
$${{{J_1}} \over {{J_2}}} = {1 \over {\cos 45^\circ }} = \sqrt 2 $$
Ball (a) $$\left| {\overrightarrow {\Delta p} } \right|$$ = 2mu = J1
Ball (b) $$\left| {\overrightarrow {\Delta p} } \right|$$ = 2mu cos45$$^\circ$$ = J2
$${{{J_1}} \over {{J_2}}} = {1 \over {\cos 45^\circ }} = \sqrt 2 $$
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