Given, initial volume of earth, Vi=V Final volume of earth, Vf=V∕8 and Ri,Rf are initial and final radii of earth. From Kepler's third law of planetary motion, T2∝R3. . . (i) where, T is time-period. Since, volume, V=
4
3
πR3 ∴V∝R3 ⇒
Vi
Vf
=
V
V
8
=
(
4
3
)π
(
4
3
)π
Rf3
Rf3
⇒8=(
Ri
Rf
)3⇒
Ri
Rf
=2 By using law of conservation of angular momentum, Li=Lf where, Li,Lf are initial and final angular momentum, respectively. Iiωi=Ifωf where, Ii,If and ωi,ωf are initial and final moment of inertia and angular speed, respectively. ⇒Ii