# If energy(E), velocity (V) and force (F) be taken as fundamental quantity, then what are the dimension of mass ?

The quantities that are independent of other quantities are called fundamental quantities. The units that are used to measure these fundamental quantities are called fundamental units. There are four systems of units namely C.G.S, M.K.S, F.P.S, and SI.The quantities that are derived using the fundamental quantities are called derived quantities. The units that are used to measure these derived quantities are called derived units.Dimensions of a physical quantity are the powers to which the fundamental units are raised to obtain one unit of that quantity.

[E]=ML2T−2

[v]=M0L1T−1

[F]=M1L1T−2

Let dimension of mass in E is=x

Let dimension of mass in V is=y

Let dimension of mass in F is=z

Then, M = Ex Vy Fz

M1L0T0 = [ML2T−2] x [M0L1T−1 ] y [M1L1T−2] z

M1L0T0 =Mx+z L2x+y+z T−2x−y−2z

x+z=1……………(i)

2x+y+z=0………(ii)

2x+y+2z=0…….(iii)

By equation (i), (ii) & (iii)

x=1 y=−2 z=0

So, [M]=E1V−2 .

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