The potential energy of a particle varies with distance x from a fixed origin as U = (A√x)/( x2+B), where A and B are dimensional constants , then find the dimensional formula for AB.

Solution:

Given U = (A√x)/( x2+B)

x is the distance .

Unit of B is equal to unit of x2 = [L2]

B = [L2]

U = A[x1/2]/(x2+B)

[ML2T-2] = A[L1/2]/[L2]

A = [ML7/2T-2]

AB = [ML7/2T-2][L2]

= [ML11/2T-2]