JEE Main 20199 AprilMorning Shift

Exam: JEE Main
Year: 2019
Date: 9 April
Shift: Morning Shift
Subject: Physics
Chapter: Center of Mass, Momentum and Collision

JEE Main 2019 · 9 April · Morning Shift · Physics · Center of Mass, Momentum and Collision

A body of mass 2kg makes an elastic collision with a second body at...

A body of mass

2kg

makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body? A body of mass 2kg makes an elastic collision with a second body at rest and continues to move in the original

A body of mass 2kg makes an elastic collision with a second body at rest and continues to move in the original

Options

A $1.8kg$
B $1.2kg$
C $1.0kg$
D $1.5kg$

Correct answer

B. $1.2kg$

Step-by-step solution

From conservation of linear momentum

mU = m\dfrac{U}{4} + MV

. . . (i)
For elastic collision:

e = 1 = \dfrac{V - \dfrac{U}{4}}{u}

V = \dfrac{5U}{4}

. . . (ii)
From equation (i) & (ii),

mU = m\dfrac{U}{4} +

M\left(\dfrac{5U}{4}\right)

<br/>

m = \dfrac{m}{4} + \dfrac{5}{4}M ⇒ M = \dfrac{3m}{5} = 1.2kg

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