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

Answer

D

Explanation

Dimensions of `beta^(3)=` Dimensions of density `=[ML^(-3)]`
`implies[beta]=[M^(1//3)L^(-1)]`
Also `[alpha]`=[Force]`xx` [Density]
`[MLT^(-2)][ML^(-3)]=[M^(2)L^(-2)T^(-2)]`