Keeping the radius of the earth unchanged if the mass of the earth is doubled , then what will be the length of a day?

Explanation

If the present angular velocity is `omega` and the changed angular velocity is `omega`, then according to the principle of conservation of angular momentum,
`Iomega= I.omega`.
[ here `I` and `I.` are the present and the changed moments of inertia of the earth respectively ]
`:. " " (2)/(5) MR^(2)xx(2pi)/(24)=(2)/(5) xx2M xxR^(2)xx(2pi)/(T.)`
[ here the present mass of the earth is M, its radius is R and the changed length of a day is T. ]
or, `(1)/(24)=(2)/(T.)or,T.`=48 hours
So, the length of a day will be 48 h.