Question

If energy `(E )` , velocity `(V)` and time `(T)` are chosen as the fundamental quantities , the dimensions formula of surface tension will be
A. `[EV^(-2)T^(-1)]`
B. `[EV^(-1)T^(-2)]`
C. `[EV^(-2)T^(-2)]`
D. `[E^(-2)V^(-1)T^(-3)]`

Answer 1

Correct Answer - c
Let surface tension `[e] = [E^(x)V^(y)T^(z)]`
we have `[x] = [MT^(-2)]`
`[E] = [ML^(2)T^(-2)], [V] = [LT^(-1)] and [T] = [T]`
`rArr [S] = [ML^(2)T^(-2)]^(x) [LT^(-1)]^(y) [T]^(z)`
`[M^(1)L^(0)T^(-2)] = [M^(x)L^(2x +y)T^(-2x -y +z)]`
`x = 1`
`2x + y = 0 rArr y = -2`
`-2x - y + z = -2`
`rArr -2 xx 1 - (-2) + z = -2`
`rArr z = -2`
Hence `[s] = [EV^(-2)T^(-2)]`