The potential energy of a particle varies with distance x from a fixed origin as `V= (Asqrt(X))/(X + B)` where A and B are constants . The dimension of AB are

Options

A. `[M^(1)L^(5//2)T^(2)]`
B. `[M^(1)L^(2)T^(2)]`
C. `[M^(3//2)L^(5//2)T^(2)]`
D. `[M^(1)L^(7//2)T^(2)]`

Answer

D

Explanation

`B = x -[L] ,A sqrt(x) = Vx, A = V sqrt(x)`
` = ML^(2)T^(-2)L^(1//2) = ML^(5//2)T^(-2)`
`AB = (ML^(5//2) T^(-2))(L) =[M^(1)L^(7//2)T^(-2)]`