Question Paper from: JEE Main 2021 - Paper 1

A particle of mass m moving with speed v collide elastically with the end of a uniform rod of mass M and length L perpendicularly as shown in the figure. If the particle comes to rest after the collision. The ratio of masses $(\frac{n}{M}) i s$ \frac{1}{x} $. T h e v a l u eo f$ x$$ is ...........

Correct Answer :

Solution:

Chapter Name: Collision,Conservation of Momentum

Difficulty Level: Moderate

Conservation of angular momentum about the center of mass of the rod

$m v (\frac{L}{2}) = \frac{M L ^{2}}{12} (ω)$ . . . . . .(i)

$m v = M v_{1}$ . . . . . . . .(ii)

$1 = \frac{v _{1} + ω \frac{L}{2}}{v}$ . . . . . . . . . . (iii)

putting $v_{1}$ from (ii) and $ω L$ from (i) in (iii)

$v = \frac{m}{M} v + \frac{6 m v}{2 M}$

$1 = \frac{4 m}{M}; \frac{m}{M} = \frac{1}{4}$

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