Question

The kinetic energy K of a rotating body depends on its moment of inertia I and its angular speed `omega`. Assuming the relation to be `K=kI^(alpha) omega^b` where k is a dimensionless constatnt, find a and b. Moment of inertia of a spere about its diameter is `2/5Mr^2`.

Answer 1

Correct Answer - A::B
`K=KI^aomega^b
where K=` kinetic energy of rotating body and kk= dimensionless constant Dimensions of left side are `K=[ML^2T^-2]`Dimensions of right side are `I^a=[ML^2}^a, omega^b=[T^-1]^b`
According to principle of homogeneity of dimension
`[ML^2T^-2]=[ML^2][T^-1]^b` Equatin the dimensions of both sides wer get `2=2a and -2=-b
alpha =1 and b=2`