Question

If earth suddenly contracted to half its radius without any change in its mass and shape duration of day will be

Answer 1

moment of inertia(I) is proportional to radius^2 ang. vel (w1) = 2pi/24 i.e pi/12 Let r1 =r r2 =0.5r By law of conservation of angular momentum, I1x w1=I2xw2 I1/I2 = w2/w1 r^2/(0.5 r)^2 = w2/(pi/12) w2=pi/3 so, time period = 6hours"

Answer 2

The duration will be 6 hours

Correct answer:- Option C ( 6 Hours )

Explanation:-

In this, The angular momentum of the earth will be stable/constant. And, In this I will be proportional to the Radius of the earth.

I = Inertia

According to the question, radius of the earth is reduced to half of its original size. It means that, Earth radius is reduced in its 4 parts.

Therefore, The time taken for the earth will be 1/4th of the Earth's 24 hours.

Duration of earth = 24/4

= 6 Hours

Therefore, The duration of the day will be 6 hours.

Additional information:-

The radius of the earth is reduced by 4 times. So, the inertia (I) will be decreased to (R2) 2.

Which is = R × 2 × 2

Radius = 4 times reduced

So, 24/4 = 6 Hours