Question

The momentum of a body of given mass is proportional to:

Answer 1

Hint: The momentum of a body is the product of the mass and the velocity. Thus, the terms, momentum of a body, the mass of a body and the velocity of that body are proportional to each other and varies accordingly.
Formula used:
\[p=mv\]

Complete answer:
From the given information, we have the data as follows.
The momentum of a body of a given mass.
The momentum of a body is the product of the mass and the velocity. Thus, the terms, momentum of a body, the mass of a body and the velocity of that body are proportional to each other and varies accordingly.
The mathematical representation of the same is given as follows.
\[p=mv\]
Where p is the momentum, m is the mass and v is the velocity.
For a constant mass, the momentum of a body is proportional to the velocity of the body. The mathematical representation of the same is given as follows.
\[p\propto v\]
For a constant velocity, the momentum of a body is proportional to the mass of the body. The mathematical representation of the same is given as follows.
\[p\propto m\]
The angular momentum equals the product of the moment of inertia and the angular velocity,\[L=l\times \omega \]. The linear momentum equals the product of the mass and the velocity,\[p=m\times v\].
\[\therefore \]The momentum of a body of given mass is proportional to the velocity of that body.

Note:
There are two types of momentum, they are, the angular momentum and the linear momentum. The angular momentum equals the product of the moment of inertia and the angular velocity. The linear momentum equals the product of the mass and the velocity.