Question

The dimensional formula for impulse is:
\[\begin{align}
  & A.~~~~~~~ML{{T}^{-2}} \\
 & B.~~~~~~~ML{{T}^{-1}} \\
 & C.~~~~~~~M{{L}^{2}}{{T}^{-1}} \\
 & D.~~~~~~~{{M}^{2}}L{{T}^{-1}} \\
\end{align}\]

Answer 1

Hint: The dimensional formula of impulse can be found by using the dimensions of force and time, as impulse is integral of force, over time, for which it acts. Mathematically,
$J=\int{F\cdot dt}$ , where J is impulse, F is force and t is time.
So, to obtain the dimension of impulse we will multiply the dimension of force and time.

Complete step by step answer:
 The impulse of a force is defined as the integral of force with respect to time, for which the force acts. It can also be defined as a change in momentum of the body before and after application of the force. Impulse is represented by J.
Dimensional formula of a physical quantity is the expression of it in terms of symbols of fundamental units. It is enclosed in brackets. The fundamental units and their symbols are;
Mass [M] Length [L] Time [T] Current [A] Temperature [K] Amount of substance [mol] Luminous intensity [J]

Impulse of the force is the integral of force, over time, for which it acts. Mathematically we can write
$J=\int{F\cdot dt}$
The dimension of force is
$ML{{T}^{-2}}$
The dimension of time is
\[{{M}^{0}}{{L}^{0}}{{T}^{1}}\]
 So, the dimension of impulse will be
$ML{{T}^{-1}}$
Hence the correct option is B.
Note: Impulse is a derived quantity, so its dimension is made from the dimension of base S.I. units. The S.I. base units are also known as fundamental units. Even if the power of dimension of length, time, and mass in a physical quantity is zero, it is recommended to mention them.