An asteroid of mass M is approaching earth, initially at a distance of $10 R_{e}$ with speed $V_{i}$ . It hits the earth with a speed $V_{f}$ (Consider $R_{e}$ and $M_{e}$ as radius and mass of the earth), then:

Q. A particle is released at a height

r_{E}

(radius of earth ) above the earth 's surface. Determine its velocity when it hits the earth. Ignore air resistance.

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An object is released from rest at a distance of 2vre from the center of the Earth, where re is the radius of the Earth. In terms of the gravitational constant (G ), the mass of the Earth (M ), and re, what is the velocity of the object when it hits the Earth?

The correct option is D √GM/reWhen the object falls from height 2re to re, the loss in gravitational potential energy would be equal to the gain in kinetic energy.Hence −GMm2re−(−GMmre)=12mv2⟹GMm2re=12mv2⟹v=√GMre

An object is released from rest at a distance of $2 v r_{e}$ from the center of the Earth, where $r_{e}$ is the radius of the Earth. In terms of the gravitational constant (G ), the mass of the Earth (M ), and $r_{e}$ , what is the velocity of the object when it hits the Earth?