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There are two bodies of masses $m$ and $3 m$ moving with a velocity of $3 v$ and $v$ respectively, moving along the same direction, collide with each other. They stick together after collision and move with a velocity $V$ in the same direction then,

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V = v

V = 3 / 2 v

V = 2 v

V = 4 / 3 v

answer is B.

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Detailed Solution

There are two bodies of masses

m

, and

3 m

, and with a velocity

3 v

and

v

respectively, moving along the same direction, collide with each other. They stick together after collision and move with a velocity

V

in the same direction then,

V = \frac{3}{2 v} .

Given:
Mass of two bodies

M_{1} = m

and

M_{2} = 3 m

Initial velocity of the two bodies

u_{1} = 3 v

and

u_{2} = v

By the law of conservation of linear momentum,

P_{f} = P_{i}

, where

P_{f}

is the final momentum and

P_{i}

is the initial momentum.

\Rightarrow mV + 3 mV = m (3 v) + 3 m (v)

\Rightarrow 4 mV = 6 mv

\Rightarrow V = \frac{3}{2} v

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