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Suppose the earth suddenly shrinks in si...

Suppose the earth suddenly shrinks in size, still remaining spherical and mass unchanged (All gravitational forces pass through the centre of the earth).

A

The days will become shorter.

B

The kinetic energy of rotation about its own axis will decrease

C

The duration of the year will increase

D

The magnitude of angular momentum about its axis will increase.

Text Solution

Verified by Experts

The correct Answer is:
A
`I_(1)omega_(1)=I_(2)omega_(2)` (Angular momentum is conserved)
As `I_(2)` decreases `omega_(2)` increases.
Thus `T=(2pi)/(omega)` i.e. `T` decreases
Therefore the earth is completing each circle around its own axis in lesser time.
`K.E.=1/2Iomega^(2)` Therefore `K.E.` of rotation increases.
Duration of the year is dependent upon time taken to complete one revolution around the sun.
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