Question

The SI unit of linear momentum is _ _ _ _ _ _.
$\text{A}\text{. }m{{s}^{-1}}$
$\text{B}\text{. }kg{{s}^{-1}}$
$\text{C}\text{. kg}m{{s}^{-1}}$
$\text{D}\text{. kg}m$

Answer 1

Hint: Momentum of a body is defined as the product of its mass and its velocity. Hence, momentum p of a body in motion is given as p = mv, where m is the mass of the body and v is its velocity. Use this expression of momentum to find its SI units.

Complete step by step answer:
When a body is in motion, we say that the body has some momentum. Momentum of a body is defined as the product of the mass of the body and the velocity of the body. Suppose a body of mass m is moving with a velocity v then its momentum (p) is equal to p=mv.
Since momentum depends on velocity of the body, it has a specific direction. Therefore, it is a vector quantity. The direction of momentum is along the direction of velocity.
The dimensional formula of momentum p will be $\left[ p \right]=\left[ mv \right]$.
We know that the dimensional formula of mass m is [M].
Since velocity is equal to displacement upon time, the dimensional formula of velocity v is $\left[ L{{T}^{-1}} \right]$.
Therefore, $\left[ p \right]=\left[ mv \right]=\left[ M \right]\left[ L{{T}^{-1}} \right]=\left[ ML{{T}^{-1}} \right]$
Hence, the dimensional formula of momentum is $\left[ ML{{T}^{-1}} \right]$.
With the help of the dimensional formula, let us calculate the SI unit of momentum.
SI units of mass, length and time are kg, m and s respectively.
Therefore, the SI unit of momentum is $kgm{{s}^{-1}}$.
Hence, the correct option is C.

Note: To find the units of a physical quantity, we can also substitute the units of the quantities given in the expression of that physical quantity and simply it.
Let us take the given problem as an example. Here, p=mv. We know the units of m and v are kg and $m{{s}^{-1}}$. Therefore, the units of p will be $kg.m{{s}^{-1}}$.