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Byju's Answer

Standard IX

Physics

Velocity of COM

A nucleus mov...

Question

A nucleus moving with a velocity $\to v$ emits an $α$ -p article. Let the velocities of the $α$ -particle and the remaining nucleus be $_{1}$ and $_{2}$ and their masses be $m_{1}$ , and $m_{2}$ respectively. Choose the correct option.

, and must be parallel to each other.

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None of the two of , and should be parallel to each other.

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+ must be parallel to .

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must be parallel to .

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Solution

The correct option is D
must be parallel to .

If initially the nucleus is moving with a velocity $\to v$ , then considering the nucleus as a point mass,
its centre of mass is moving with $\to v$ .
Now after the disintegration of nucleus into $α$ -particle and the residual, the COM should be moving with the same velocity as there is no net external force acting upon it.
And we also know,
${\to v}_{C M} = \frac{m_{1}_{1} + m_{2}_{2}}{m_{1} + m_{2}}$
Which clearly shows that ( $m_{1}_{1} + m_{2}_{2}$ ) must be parallel to $\to v$ .

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Q. A nucleus moving with a velocity

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(a)

\vec{v}, {\vec{v}}_{1} and {\vec{v}}_{2}

must be parallel to each other.
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A nucleus moving with a velocity $\to v$ emits an $α$ -p article. Let the velocities of the $α$ -particle and the remaining nucleus be $_{1}$ and $_{2}$ and their masses be $m_{1}$ , and $m_{2}$ .

A nucleus moving with a velocity $\to v$ emits an $α$ -p article. Let the velocities of the $α$ -particle and the remaining nucleus be $_{1}$ and $_{2}$ and their masses be $m_{1}$ , and $m_{2}$ respectively. Choose the correct option.