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JEE Advanced 2009Paper 2

Exam: JEE Advanced
Year: 2009
Paper: Paper 2
Subject: Physics
Chapter: Center of Mass, Momentum and Collision

JEE Advanced 2009 · Paper 2 · Physics · Center of Mass, Momentum and Collision

Three objects A, B and C are kept in a straight line on a...

Three objects

A, B

and

C

are kept in a straight line on a frictionless horizontal surface. These have masses

m, 2 m

and

m

, respectively. The object

A

moves towards

B

with a speed

9 \mathrm{~ms}^{-1}

and makes an elastic collision with it. Thereafter,

B

makes completely inelastic collision with

C

. All motions occur on the same straight line. Find the final speed (in

\mathrm{ms}^{-1}

) of the object

C

.

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses m, 2 m and

Correct answer

4

Step-by-step solution

After elastic collision,

\begin{aligned}v_A^{\prime} & =\left(\frac{m-2 m}{m+2 m}\right)(9)+\frac{2(2 m)}{m+2 m}(0) \\ & =-3 \mathrm{~ms}^{-1} \end{aligned}

Now from conservation of linear momentum after all collisions are complete,

\begin{array}{rlrl}m\left(+9 \mathrm{~ms}^{-1}\right)& =m\left(-3 \mathrm{~ms}^{-1}\right)+3 m\left(v_C\right) \\ & \text{ or } \quadv_C & =4 \mathrm{~ms}^{-1} \end{array}

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