Question

`( alpha)/( t^(2)) = Fv + ( beta)/(x^(2))`
Find the dimension formula for `[ alpha] and [ beta]` ( here t = time , F = force , v = velocity , x = distance).

Answer 1

Correct Answer - `[beta] = M^(1) L^(4) T^(-3) ; [alpha] = M^(1) L^(2) T^(-1)`
Since `[Fv] = M^(1) L^(2) T^(-3)`,
So `[ (beta)/( x^(2))]` should also be `M^(1) L^(2)T^(-3)`
`[beta] = M^(1) L^(4) T^(-3) and [Fv + ( beta)/( x^(2))]` will also have dimension
`M^(1)L^(2) T^(-3)`. So,
`([alpha)]/([ t^(2)]) = M^(1) L^(2)T^(-3) , [alpha] = M^(1) L^(2) T^(-1)`