Question

S.I. unit of momentum is:
A. \[kg.m{{s}^{-1}}\]
B. \[kg.m{{g}^{-2}}\]
C. \[kg.m{{g}^{2}}\]
D. \[kg.{{m}^{-1}}{{s}^{-1}}\]

Answer 1

Hint: In mechanics, linear momentum or momentum is the product of the mass and velocity of an object. Mathematically it is given by, \[p=mv\]. For finding the S.I. unit we need to write the S.I. unit of each and every quantity on the right hand side and simplify.

Complete step by step answer:

Linear Momentum: The linear momentum of a particle of mass m moving with a velocity is defined to be the product of the mass and velocity.

Mathematically, \[\overrightarrow{p}=m\overrightarrow{v}\]

The terms momentum and linear momentum are used interchangeably in various books.
Linear momentum is a vector quantity. Its direction is the same as the direction of the velocity of the body.

The dimensional formula of momentum is \[\left[ ML{{T}^{-1}} \right]\]

 The S.I. unit of momentum is \[kg.m{{s}^{-1}}\]

Hence, the correct option is A, i.e., \[kg.m{{s}^{-1}}\]

Additional Information:
Newton’s Second Law relates the momentum of a particle to the resultant force acting on it. The rate of change of linear momentum of a particle is equal to the net force acting on it.

\[\sum{\overrightarrow{F}}=m\overrightarrow{a}=m\dfrac{d\overrightarrow{v}}{dt}=\dfrac{d\left( m\overrightarrow{v} \right)}{dt}=\dfrac{d\overrightarrow{p}}{dt}\]

This is the format in which Newton presented the Second Law.

Note: Students need to know the formula for momentum i.e., \[p=mv\] so that they can write the unit of the physical quantities present in this mathematical expression, and in this way find the S.I. unit of the momentum. Students should be very careful while doing simplification, after writing units of each quantity because if they make even a small mistake, then among options that answer may be available.