JEE Main 202118 MarchMorning Shift

Exam: JEE Main
Year: 2021
Date: 18 March
Shift: Morning Shift
Subject: Physics
Chapter: Center of Mass, Momentum and Collision

JEE Main 2021 · 18 March · Morning Shift · Physics · Center of Mass, Momentum and Collision

A ball of mass 10kg moving with a velocity 10 3 m s ^ - 1 along the...

A ball of mass $10kg$ moving with a velocity $10\sqrt{3}m{s}^{- 1}$ along the $x$ -axis, hits another ball of mass $20kg$ which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along $y$ -axis with a speed of $10m{s}^{- 1} .$ The second piece starts moving at an angle of $30 °$ with respect to the $x$ -axis. The velocity of the ball moving at $30 °$ with $x$ -axis is $xm{s}^{- 1} .$ The configuration of pieces after the collision is shown in the figure below. The value of $x$ to the nearest integer is

A ball of mass 10kg moving with a velocity 10 3 m s ^ - 1 along the x -axis, hits another ball of mass 20kg which is at

Correct answer

Step-by-step solution

Let the velocity of

{2}^{\text{nd}}

fragment is

\overset{\to}{v}

then by conservation of linear momentum

10 ( 10\sqrt{3} ) \overset{^}{i} = ( 10 ) ( 10\overset{^}{j} ) + 10\overset{\to}{v}

⇒ \overset{\to}{v} = 10\sqrt{3}\overset{^}{i} - 10\overset{^}{j}

| \overset{\to}{v} | = \sqrt{300 + 100} = \sqrt{400} = 20m{s}^{- 1}

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