JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Conservation of Momentum

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Two billiard balls of equal mass 30 g 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:

(A) $2 : 1$ ✓ Correct
(B) $1 : 2$
(C) $1 : 1$
(D) $2 : 1$

Answer: (A)

Solution

Impulse is the change in momentum. For ball (a) striking perpendicular to the wall, the impulse along X-direction is

I_{1} = Δ p_{1} = 2 m u

(velocity reverses completely). For ball (b) striking at

4 5^{\circ}

, only the X-component of velocity reverses, so

I_{2} = Δ p_{2} = 2 m u cos 4 5^{\circ} = 2 m u / 2 = 2 m u

. Therefore,

\frac{I _{1}}{I _{2}} = \frac{2 m u}{2 m u} = 2

, giving the ratio

2 : 1

JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Single correct option

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JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Conservation of Momentum

Solution

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