Question

If velocity p, acceleration q and density r are taken
as fundamental quantities, then the dimensional
formula for kinetic energy k is
​

Answer 1

Explanation is written in the image linked above.

Answer 2

Dear Students,

● Answer -

[K.E.] = [p]^8.[q]^-3.[r]^1

◆ Explaination -

Dimensional formula of kinetic energy is given by -

[K.E.] = [p]^x.[q]^y.[r]^z

[L2M1T-2] = [L1M0T-1]^x.[L1M0T-2]^y.[L-3M1T0]^z

[L2M1T-2] = [L]^(x+y-3z).[M]^(0+0+z).[T]^(-x-2y+0)

Comparing indexes on two sides -

x + y - 3z = 2

z = 1

-x - 2y = -2

Solving these equations,

x = 8

x = 8y = -3

x = 8y = -3z = 1

Thus, dimensional formula of kinetic energy is [p]^8.[q]^-3.[r]^1 .

Hope this helped you. Keep asking..