Question

The potential energy of a particle varies with distance as `U= (Asqrt(x))/(x^2 + B)`, where A and B are constants. The dimensional formula for `A * B` is?

Answer 1

Dimension of A is equals to dimension of `{U(x^2+B)}/sqrtx` or `[M L^2 T^-2].[L^2]/[L^(1/2)]` i.e `[M L^(7/2) T^-2]`

And dimension of B is equals square of `x` that is `[L^2]` (because two quantities can be added only when their dimension is the same)

So dimension of `A.B` will be `[M L^(11/2) T^-2]`