Question

What are the dimensions of A/B in the relation F = A√x + Bt^2,

Answer 1

F = A√x + Bt^2

Dimension of force = [M L T^(-2)]

i) Dimension of A√x = Dimension of force = [M L T^(-2)]

Dimension of √x = [L^(1/2)]

Dimension of A = [M L T^(-2)] ÷ [L^(1/2)] = [ M L^(1 - 1/2) T^(-2) ] = [M L^(1/2) T^(-2)]

Dimension of A = [M L^(1/2) T^(-2)]

ii) Dimension of Bt^2 = Dimension of force = [M L T^(-2)]

Dimension of t^2 = [T^(2)]

Dimension of B = [M L T^(-2)] ÷ [T^(2)] = [ M L T^(-2-2) ] = [M L T^(-4)]

Dimension of B = [M L T^(-4)]