The kinetic energy of rotation K depends on the angular momentum J and moment of inertia I. Find the expression for kinetic energy.

Explanation

Let `X prop J^(a)I^(b)` then,
`K=CJ^(a)I^(b)" ….(1)"`
Writing dimensions of both sides,
We get,
`[ML^(2)T^(-2)]=[ML^(2)T^(-1)]^(a).[ML^(2)]^(b)`
`[ML^(2)T^(-2)]=[M^(a+b)L^(a+b)L^(2a+2b)T^(-a)]`
Comparing powers of T, we get `-a=-2 or a=2`
Comparing powers of M, we get `a+b=1 or 2+b=1 or b=-1`
Putting these values of 'a' and 'b' in equation (1)
We get, `K=(CJ^(2))/(I)`
The value of constant C cannot be found.