JEE Main 202127 AugustEvening Shift

Exam: JEE Main
Year: 2021
Date: 27 August
Shift: Evening Shift
Subject: Physics
Chapter: Center of Mass, Momentum and Collision

JEE Main 2021 · 27 August · Evening Shift · Physics · Center of Mass, Momentum and Collision

A bullet of 10g , moving with velocity v , collides head-on with...

A bullet of $10g$ , moving with velocity $v$ , collides head-on with the stationary bob of a pendulum and recoils with velocity $100m{s}^{- 1}$ . The length of the pendulum is $0 . 5m$ and mass of the bob is $1kg$ . The minimum value of $v\text{in}m{s}^{- 1}$ , so that the pendulum describes a circle. (Assume the string to be inextensible and $g = 10m{s}^{- 2}$ )

A bullet of 10g , moving with velocity v , collides head-on with the stationary bob of a pendulum and recoils with

Correct answer

400

Step-by-step solution

Final velocity of system (bullet $+$ mass) should be $= \sqrt{5gr}$

Now $M\sqrt{5gr} = m ( v + 100 )$

thus $v = \dfrac{M}{m}\sqrt{5gr} - 100 = 500 - 100 = 400m{s}^{- 1}$

$v = 400m{s}^{- 1}$

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