r2=1/2 r1
m1=m2=m(say)
T1=24hr
By the conservation of angular momentum,
I1 ω1 = I2ω2. . . . . . . . .(1)
Where, ω=2π/T ,angular velocity of the earth
I=2/5 mr² moment of inertia of earth.
From equation (1),
2/5 mr1².2π/T1=2/5mr2².2π/T2
r1²/T1=r2²/T2
T2/T1=(r2/r1)²=(r1/2r1)²=1/4
T2=T1/4
T2=24 hr /4 = 6hr