Given : force `= (alpha)/("density" + beta^3).` What are the dimensions of `alpha, beta ?`

Options

A. `ML^(-2) T^(-2) , ML^(1//2)`
B. `M^2 L^4 T^(-2), M^(-1//3) L^(-1)`
C. `M^2 L^(-2) T^(-2) , M^(1//3) L^(-1)`
D. `M^2 L^(-2) T^(-2), ML^(-3)`

Answer

C

Explanation

`beta^2` = density = `M^2 L^(-3)`
`beta = M^(1//3) L^(-1)`
Also, `alpha = " force" xx " density" `
`= MLT^(-2) xx M^1 L^(-3) = [M^2 L^(-2) T^(-2)]`