Force F and density D are related as `F=(alpha)/(beta+sqrtd)`, Then find the dimensions of `alpha` and `beta`

Options

A. `[L^((1)/(2))M^((3)/(2))T^(-2)]`
B. `[L^(-1)M^((1)/(2))T^(-2)]`
C. `[L^(-1)M^((3)/(2))T^(-2)]`
D. `[L^(-(1)/(2))M^((1)/(2))T^(-2)]`

Answer

A

Explanation

The dimessions of force `[F] = [ML T^(-2)]` and density `[d] = [ML^(-3) T^(0)]`
From the given relation, `F =(y)/(sqrt(d))`
`rArr " " y = F sqrt(d)`
Substituting the above dimesions, we get
` [y] = [F] [d]^(1//2) = [ML T^(-2)] [ML^(-3) T^(0)]^(1//2)`
` = [M^(3//2) L^(-1//2)T^(-2)]`