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JEE Main 202125 JulyMorning Shift

Exam: JEE Main
Year: 2021
Date: 25 July
Shift: Morning Shift
Subject: Physics
Chapter: Laws of Motion

JEE Main 2021 · 25 July · Morning Shift · Physics · Laws of Motion

Two billiard balls of equal mass 30g strike a rigid wall with same...

Two billiard balls of equal mass $30g$ strike a rigid wall with same speed of $108kmph$ (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:

Two billiard balls of equal mass 30g strike a rigid wall with same speed of 108kmph (as shown) but at different angles.

Options

A $1: 1$
B $\sqrt{2}: 1$
C $2: 1$
D $1: \sqrt{2}$

Correct answer

B. $\sqrt{2}: 1$

Step-by-step solution

Impulse = change in momentum

Ball (a) $| \overset{\to}{\Deltap} | = 2mu = {J}_{1}$

Ball (b) $| \overset{\to}{\Deltap} | = 2mucos45 ° = {J}_{2}$

$\dfrac{{J}_{1}}{{J}_{2}} = \dfrac{1}{\cos 45 °} = \sqrt{2}$

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