Question

If velocity, force and time are taken to be fundamental quantities find dimensions formula for (1) mass –

• A. KV^–1FT^–1
• B. KV^–1FT
• C. KVF^–1T^–1
• D. KV^–1F^–1T

Answer 1

Answer: (B)

KV^–1FT

Answer 2

Let the mass in represented by M then

M = f (V,F,T)

Assuming that a function is product of power functions of V, F and T

M = KV^xF^yT^z

Where k is a dimension less constant of proportionality. The above equation dimensionally becomes.

[M] = [LT^–1]^x [MLT^–2]^y[T]²

i.e. [M] = [M^y] [L^{x + y}T^{–x – 2y + z}]

So equation becomes

[M] = [M^y L^{x + y} T^{–x – 2y + z}]

For dimentionally correct expression,

y = 1, x + y = 0 and –x – 2y + z = 0

Ž x = –1, y = 1 and z = 1.

Therefore M = KV^–1 FT.

Hence correct answer is (2).