The potential energy of a particle varies with distance x from a fixed origin as `u=(Asqrtx)/(x+B)`, where A and B are constants The dimensions of A and B are respectively

Options

A. `M^(1)L^(7//2)T^(-2)`
B. `M^(1)L^(1//2)T^(-2)`
C. `M^(1)L^(5//2)T^(-2)`
D. `M^(1)L^(9//2)T^(-2)`

Answer

B

Explanation

In the expression `U=(Asqrt(x))/(x^(2)+B)`
B must have the dimensions of `x^(2)` i.e.`[L^(2)]`
Dimensions of `A=(Ux^(2))/(sqrt(x))=((ML^(2)T^(-2))L^(2))/(L^(1//2))=[ML^(7//2)T^(-2)]`
`:.AB=[ML^(7//2)T^(-2)]L^(2)=[M^(1)L^(11//2)T^(-2)]`