Question

Write the dimensional formula of force
A. MLT
B. MLT$^{-2}$
C. MLT$^{2}$
D. None of the above

Answer 1

First we have to figure out the conventional formula for force. After that we have to break that formula into its individual constituents. Then relate all the individual constituents to their dimensional form, then bring all those dimensional forms into the equation of force.

Complete step-by-step answer:
[M] = MASS.
[L] = LENGTH.
[T] = TIME.
We know that,
Force= Mass $\times$ acceleration,
Now, we also know that,
Force=Mass $\times$velocity/time.
Therefore according to problem, changing all the factors of the equations to dimensional forms,
Velocity=LT$^{-1}$ ,
Mass= M
Time= T
Therefore acceleration= L/T$^{2}$
On placing the dimensional values in the equation we get,
Force= [M] $\times$ L/T$^{2}$
Therefore dimensional formula of force is,
Force= ML T$^{-2}$.
Therefore option B is the correct option.

Additional Information:
The equation that we get, when we equate a physical quantity with its dimensional formula is known as Dimensional analysis.
While doing dimensional analysis one of the most important things to remember is that the unit you wish to cancel out must be on the opposite side of the fraction.

Note: We know that the formula for force is the product of mass and acceleration, now we also know that acceleration is velocity divided by time, Now in dimensional analysis velocity is length (L) divided by (T), and acceleration is (L)/ T$^{2}$. Because acceleration is velocity/time, in this way we have to figure out the answer, break all the terms individually at first because there is a slight chance of mistake there while writing.