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
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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