Question

1. The potential energy U of a particle varies with
distance x from origin as
U = (A* x^3/2)/B + x^3
where A and
B are dimensional constants, then dimensional
formula of
(1) [ML 1/2T-2]
(2) [MOLOT-2]
3) [ML7/2T-2]
(4) [ML3/2T-2] ​

Answer 1

Answer:

this is D.F of A/B [ML^1/2T-2]

Explanation:

U = (A x^3/2)/ B +x^3

form principle of homogenity

B = [ L^3 ]

and by substituting U and B

U = [ ML^2 T^-2]

substitute it

[ML^2T^-2] × [ L^3 ] = A [ L^3/2 ]

[ ML^5 T^-2 ] / [ L^3/2 ] = A

[ ML^7/2 T ^-2 ] = A

A/B =

=[ ML^7/2 T^-2 ] / [ L^3/2 ]

=[ ML^1/2 T^-2 ]