Question

A thin uniform rod of length $2 m$, cross sectional area ' $A$ ' and density ' $d$ ' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity $\omega$ If value of $\omega$ in terms of its rotational kinetic energy $E$ is $\sqrt{\frac{\alpha Ad }{ Ad }}$ then value of $\alpha$ is _____

Answer 1

The correct answer is 3.
(KE)Rotational ​=21​Iω2=E
E=21​12mℓ2​ω2
E=21​12dAℓ3​ω2
E=24dA(2)3​ω2
dA3E​​=ω
α=3