Suppose that an asteroid traveling straight toward the center of the earth were to collide with our planet at the equator and bury itself just below the surface. what would have to be the mass of this asteroid, in terms of the earth’s mass m, for the day to become 25.0% longer than it presently is as a result of the collision? assume that the asteroid is very small compared to the earth and that the earth is uniform throughout.

M

Explanation:

To apply the concept of angular momentum conservation, there should be no external torque before and after

As the asteroid is travelling directly towards the center of the Earth, after impact ,it does not impose any torque on earth's rotation, So angular momentum of earth is conserved

⇒

let  

since

⇒ if time period is to increase by 25%, which is times, the angular velocity decreases 25% which is  times

therefore

(moment of inertia of solid sphere)

where M is mass of earth

           R is radius of earth

(As given asteroid is very small compared to earth, we assume it be a particle compared to earth, therefore by parallel axis theorem we find its moment of inertia with respect to axis)

where is mass of asteroid

⇒

= +

⇒