Question

a particle of mass m is located in a region where its potential energy [U(x)]depends on the position x as potential energy [U(x)] = a/x2-b/x here a and b are positive constants.....

write dimensional formula of a and b.

QUALITY REQUIRED

Answer 1

Potential energy , U=((A)x1/2)/(x+B)U=((A)x1/2)/(x+B)

We know dimension for energy [U]=[ML2T−2ML2T−2]

For two quantities to be added the have to be the same dimension. Hence B has dimensions of x.

=> [B]=L

Hence [U]=[[ML2T−2]=(([A])L1/2/L)ML2T−2]=(([A])L1/2/L)

=[A]L−1/2=[A]L−1/2

=> [A]=ML5/2T−2