Question

If velocity p, acceleration q, density r are taken as fundamental quantity then dimensional formula of kinetic energy k is

Answer 1

Explanation is written in the image linked above.

Answer 2

dimension of velocity, p = [LT-¹]

dimension of acceleration , q = [LT-²]

dimension of density, r = [ML-³]

and dimension of kinetic energy , K = [ML²T-²]

by dimension analysis,

dimension of K = X × dimension of {P^aq^br^c}

where X is proportionality constant.

or, [ML²T-²] = X[LT-¹]^a × [LT-²]^b × [ML-³]^c

or, [ML²T-²] = X[M^cL^(a+b-3c)T^(-a-2b)]

comparing both sides,

c = 1....(1)

a + b - 3c = 2 ....(2)

-a - 2b = -2 => a + 2b = 2 ....(3)

putting c = 1 in equation (2),

a + b - 3 = 2 => a + b = 5 ....(4)

now from equations (3) and (4),

b = -3 and a = 8

so, formula of kinetic energy ,K = $p^8q^{-3}r^1$