The potential energy of a particle varies the distance x from a fixed origin as U=A√xx2+B, where A and B are dimensional constants, then find the dimensional formula for AB.
x= distance from a fixed origin
u=A√xx2+B
unit of B is same as x2. Unit of x2=[L2]
B=[L2]
u=[x1/2]Ax2+B
A=u(x2+B)√x=kgm2s2×m2m1/2
A=kgm7/2s2
A=[ML7/2T−2]
Dimensions of AB=[ML7/2T−2][L2]
Dimensions of AB=[ML11/2T−2]