Question

A body whose momentum is constant must have constant:

• A. Force
• B. Velocity
• C. Acceleration
• D. All of these

Answer 1

The correct option is B

Velocity

Linear momentum

1. Linear momentum is the product of mass and velocity, i.e, $p=mv$, where m and v are the mass and velocity of a body.
2. Linear momentum is a vector quantity. For a rested body, linear momentum is zero.

Explanation for the correct option

Option B

1. Linear momentum is the product of mass and velocity, i.e, $p=mv$.
2. For a given mass, the linear momentum is constant means velocity is constant.
3. Since $p=mv$, here $p=cons\tan t$ and $m=cons\tan t$, so $v=cons\tan t.$

Explanation for the incorrect options

Option A

1. According 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.
2. If linear momentum is constant, then force will be zero.

Option C

1. Again we know that, force, $F=ma$, where a is the acceleration of the body.
2. If force is equal to zero, then acceleration will be zero.

So, option (B) is correct.