Question

two rotating bodies A and B of masses m and 2m with moments of inertia Ia and IB have equal kinetic

Answer 1

L= angular momentum
I = moment of inertia
w = angular velocity
Suppose Ia > Ib
​We know that
L = Iw ( formula)
Given ​angular momenta are equal:
La = Lb
Ia wa = Ibwb
wa/wb = Ib/Ia ...................(1)
this means wb >wa
K.E (kinetic energy) = 1/2 * I * w2
KEa=​1/2 * Ia * wa2
KEb=1/2 * Ib * wb2

KEa/KEb= ​Ia * wa2 / ​Ib * wb2
from eq (1)
KEa/KEb= wa/wb ................(2)
so KE of b is graeter with Inetia as Ib

Answer 2

KE = ½ IW²

we have equal KE, so that

½ IW² = ½ I'W'² (dash in place of B)____eqn 1

Angular momentum L = I W → W= L/I ____ eqn 2

subtitute the value of eqn 2 in eqn 1, we get

I×L²/I² = I'×L'²/I'²

After solving this, we get

L²/L'²= I²/l'²

According to the ques, I<l' ... now we can say that L<L'.

(Regards)