devarshi-dt-logo

Question:

If force (F), velocity (V), and time (T) are taken as fundamental units, what are the dimensions of mass?

[FVT⁻¹]

[FV⁻¹T]

[FVT]

[FV⁻¹T⁻¹]

Solution:

F = Ma = MLT⁻²
Given that force (F), velocity (V), and time (T) are fundamental units, we need to express mass (M) in terms of F, V, and T.
We know that:
F = Ma = MLT⁻²
V = LT⁻¹
T = T
From the equation for velocity, we have:
L = VT
Substituting this into the equation for force, we get:
F = M(VT)T⁻² = MVT⁻¹
Solving for M, we get:
M = FVT