If velocity [ V ], time [ T ] and force [ F ] are chosen as the base quantities, the dimensions of the mass will be:

Question

If velocity [ V ], time [ T ] and force [ F ] are chosen as the base quantities, the dimensions of the mass will be: (A) [ FT -1 V -1] (B) [ FTV -1] (C) [ FT 2 V ] (D) [ FVT -1]

Tardigrade Admin · Accepted Answer

[ M ]= K [ F ] a [ T ] b [ V ] c [ M 1]=[ M 1 L 1 T -2] a [ T 1] b [ L 1 T -1] c a =1, b =1, c =-1 ∴ [ M ]=[ FTV -1]

Q. If velocity $[V]$ , time $[T]$ and force $[F]$ are chosen as the base quantities, the dimensions of the mass will be:

$[F T^{- 1} V^{- 1}]$

$[FT V^{- 1}]$

$[F T^{2} V]$

$[F V T^{- 1}]$

$[M] = K [F]^{a} [T]^{b} [V]^{c}$
$[M^{1}] = [M^{1} L^{1} T^{- 2}]^{a} [T^{1}]^{b} [L^{1} T^{- 1}]^{c}$
$a = 1, b = 1, c = - 1$
$∴ [M] = [FT V^{- 1}]$

Q. If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be:

[FT−1V−1]

[FTV−1]

[FT2V]

[FVT−1]