Question

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

Options

• EV²

• EV^-2

• FV^-1

• FV^-2

Answer 1

EV^-2

Explanation:

M ∝ [E]^a[V]^b[F]^c .........(i)

M¹ = K[M¹L²T^–2]^a [L¹T^–1]^b [M¹L¹T^–2]^c

`"M"^1"L"^0"T"^0 = "KM"^{"a"+"c"} "L"^{2"a"+"b"+"c"} "T"^{–2"a" – "b" – 2"c"}`

a + c = 1 .........(ii)

2a + b + c = 0 ......(iii)

2a + b + 2c = 0 .......(iv)

On solving equation (ii), (iii) and (iv), we get

a = 1, b = –2, c = 0

Putting values of a, b and c in equation (i),

M = EV^–2