A particle of mass m moving with velocity v collides with a...

A particle of mass

m

moving with velocity

v

collides with a stationary particle of mass

2 \mathrm{ m}

. After collision, they stick together and continue to move together with velocity A particle of mass m moving with velocity v collides with a stationary particle of mass 2 m . After collision, they

A particle of mass m moving with velocity v collides with a stationary particle of mass 2 m . After collision, they

Options

A $\mathrm{v}$
B $\frac{\mathrm{v}}{2}$
C $\frac{\mathrm{v}}{3}$
D $\frac{v}{4}$

Correct answer

C. $\frac{\mathrm{v}}{3}$

Step-by-step solution

Applying conservation of linear momentum

\Rightarrow \overrightarrow{\mathrm{P}_{\mathrm{i}}=\overrightarrow{\mathrm{P}_{\mathrm{f}}(\because

\mathrm{P}=\mathrm{mv}

)

m v_1+2 m v_2=(m+2 m) v^{\prime}

m v^1+2 m \times 0=(3 m) v^{\prime}

\Rightarrow \mathrm{mv}=3 \mathrm{mv}^{\prime} \Rightarrow \mathrmv^{\prime}=\frac{\mathrm{v}}{3}

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