Question

# A body whose momentum is constant must have constant:

A

Force

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B

Velocity

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C

Acceleration

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D

All of these

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Solution

## The correct option is B VelocityLinear momentumLinear momentum is the product of mass and velocity, i.e, $p=mv$, where m and v are the mass and velocity of a body.Linear momentum is a vector quantity. For a rested body, linear momentum is zero.Explanation for the correct optionOption BLinear momentum is the product of mass and velocity, i.e, $p=mv$.For a given mass, the linear momentum is constant means velocity is constant.Since $p=mv$, here $p=cons\mathrm{tan}t$ and $m=cons\mathrm{tan}t$, so $v=cons\mathrm{tan}t.$Explanation for the incorrect optionsOption AAccording to Newton's second law of motion, the linear momentum is proportional to the applied force, i.e, $F\propto \frac{dp}{dt}$, where F is the applied force, P is the linear momentum.If linear momentum is constant, then force will be zero.Option CAgain we know that, force, $F=ma$, where a is the acceleration of the body.If force is equal to zero, then acceleration will be zero.So, option (B) is correct.

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