To solve this problem, use the formula for Newton’s second law of motion which gives relation between force, mass and acceleration. But acceleration can be written in terms of velocity and time. So, substitute this relation in the formula for force. Rearrange the equation and get the expression for mass of a body. Then write this obtained equation in dimensions form. This will be the dimensions of mass if force, velocity and time are taken as fundamental quantities.
Formula used:
F=MA A=‌ According to Newton's second law of motion, force is given by,
F=MA...(2) Where,
M is the mass of the body
A is the acceleration acting on the body
We know, acceleration is given by,
A=‌...(2) Where,
V is the velocity of the body
T is the times taken by the body Substituting equation. (2) in equation. (1) we get,
F=M‌ Rearranging the above equation we get,
M=F‌ ⇒[M]=[FTV−1] Hence, if force
(F), velocity
(V) and time
(T) are taken as fundamental units, the dimensions of mass are
[FV−1T]