Question

what will be duration of day with earth if shrinks to 1/64 of its original volume mass remaining unchanged​

Answer 1

Answer:

assume,

earth is solid sphere,

vi=4/3 πr³

vf=1/64 ×vi

= 4πr³/3×64

vf=4/3π (R/4)³

=4/3πr'³

=r/4=r'

earth shrink=means,no external torque I.e 0,

angular momentum is conserved,

Lbefore shrink=Lafter shrink

IiWi =IfWf

2/5MR²Wi=2/5MR²/16 Wf,

Wf=16Wi,

24hr=1 revo.=2πrad,

2πrad/24hr

2π×16/24 rad,

2π/3/2 rad/hr

3/2hr

i.e 1.5 hr or 1:30 hr