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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Physics
Chapter: Center of Mass, Momentum and Collision

NTA Abhyas 2020 · Physics · Center of Mass, Momentum and Collision

A smooth sphere of mass M moving with velocity u directly collides...

A smooth sphere of mass

M

moving with velocity

u

directly collides elastically with another sphere of mass

m

at rest. After the collision, their final velocities are

V

and

v

respectively. Then

v

is

Options

A $\dfrac{2uM}{m}$
B $\dfrac{2um}{M}$
C $\dfrac{2u}{1 + \dfrac{m}{M}}$
D $\dfrac{2u}{1 + \dfrac{M}{m}}$

Correct answer

C. $\dfrac{2u}{1 + \dfrac{m}{M}}$

Step-by-step solution

By law of conservation of momentum,

Mu = MV + mv

…(i)

e = \dfrac{| {v}_{1} - {v}_{2} |}{| {u}_{1} - {u}_{2} |} = \dfrac{v - V}{u} ⇒ e = 1 = \dfrac{v - V}{u} ⇒ u = v - V

⇒ Mu = Mv - MV

....(ii)
From (i) and (ii),

2Mu = ( M + m )v

⇒ v = \dfrac{2uM}{M + m} ⇒ v = \dfrac{2u}{1 + \dfrac{m}{M}}

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