Question

The potential energy of a particle varies with velocity v,as U=Av^3/v+B. If A and B are constant the dimensional formula of A/B is?​

Answer 1

Answer:

U= A×v^3/v+B

[ML^2T^-2]=A×[LT^-1]^3/[LT^-1]+B

According to the principle of homogeneity, similar quantities can be added or subtracted.

Therefore, Dimensions of B are same as Dimensions of velocity

B=[LT^-1]

Also if we shift the given dimensions then

A= U× (B+v)/ v^3

A= [ML^2T^-2]× [LT^-1] / [LT^-1]^3

A= [ML^3T^-2] / [L^3T^-3]

A=[M]

THUS,

A/B = M/ LT^-1

A/B = [ML^-1T]

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