The moment of inertia of a collapsing star changes to one _ third of its initial value . the ratio of the new rotational kinetic energy to the initial rotational kinetic energy is
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Hey,
Let i1 be the initial rotation and w1 the initial angular speed.
We know that angular momentum is L=I1w1
Initial kinetic energy k1=Lw1/2
after collapsing the rotational inertia decreases by 1/3, therefore new inertia will be i2=i1/3
let w2 be new angular speed.
Since the net torque is zero the angular momentum does not change after collapse that is
i1w1=i1*w2/3
w2=3w1
thus, new rotational kinetic energy after collapse is:
k2=Lw2/2=3Lw1/2
Therefore the new rotational kinetic energy to initial kinetic enrgy will be
k1/k2=(3Lw1/2)*(2/lw1)=3
Thus 3 is the required answer.
I hope this helps.
All the best!
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