Question

Momentum has the same units as that of:
A. impulse
B. torque
C. moment of momentum
d. couple

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. Change in momentum is called impulse.

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 $kgm{{s}^{-1}}$.
When a force is applied on a body, its momentum changes. The change in the momentum of the body is called impulse ($\Delta p$).
Suppose the velocity a body of mass m changes from ${{v}_{1}}$ to ${{v}_{2}}$, the impulse created in the body is $\Delta p=m{{v}_{2}}-m{{v}_{1}}$.
Since impulse is just change in momentum, the dimensional formula and unit will be the same as that of momentum.
Hence, the correct option is A.

Note: The units of other options are as follows:
(a) unit of torque is same as the unit of energy i.e. Nm.
(b) moment of momentum is called angular momentum and its unit is $kg{{m}^{2}}{{s}^{-1}}$.
(c) couple is the torque generated when two forces, equal in magnitude but opposite in direction act at two points at equal distances from the axis of rotation.