# If the radius of earth changes to half of the previous keeping the mass and shape same . Then what will its change in time period of day . Options are 1- 24hour 2- 8hour 3- 6hour 4- 12hour

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A day is the timeperiod of earth’s rotation. This is related to angular velocity of rotation of the earth. Since there is no torque involved in the question, the angular momentum would not change. Angular momentum and angular velocity are related by moment of inertia, which varies proportional to square of the earth’s radius.

Radius becomes n times, without the mass being changed.

Moment of inertia (I) becomes n*n (‘n squared’ times).

Angular momentum L = I . w (where w -angular velocity) is constant

Angular velocity w becomes 1/(n*n) times

Timeperiod T = 2*pi/w becomes n*n times again.

So, a day becomes 24*n*n hours long.

Radius becomes n times, without the mass being changed.

Moment of inertia (I) becomes n*n (‘n squared’ times).

Angular momentum L = I . w (where w -angular velocity) is constant

Angular velocity w becomes 1/(n*n) times

Timeperiod T = 2*pi/w becomes n*n times again.

So, a day becomes 24*n*n hours long.

dhananjaybarman:
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