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

Options

A. `ML^(–2) T^(–2) , ML^(–1//3)`
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), M L^(–3)`

Answer

C

Explanation

Dimension of `β^(3)` = dimension of density
Solve, `beta=[M^(1//3)L^(-1)]`
Force = `(alpha)/("density")`
`alpha` = Force `xx` density
`=[MLT^(-2)ML^(-3)]`
`=[M^(2)L^(-2)T^(-2)]`