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

The kinetic energy of rotation K depends on the angular momentum J and

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