Question

The velocity by which object m hits the earth is ____

A. (GM/R)⁰.⁵
B. 1/2× (GMm/R)
C. GMm/3R
D. (4/3 × GM/R)⁰.⁵

Answer 1

The velocity with which an object hits the Earth is given by (GM/R)¹/², derived from energy conservation principles equating gravitational potential and kinetic energies.

Step-by-step explanation:

The velocity with which an object m hits the Earth is given by the formula derived from equating kinetic energy to gravitational potential energy. Using the formula for gravitational potential energy (U = -GMm/R) and kinetic energy (K = 1/2 mv²), and setting them equal for an object falling from rest far away (ignoring air resistance), we get:

1/2 mv² = GMm/R

By canceling out the mass m from both sides and solving for v, we obtain:

v = (2GM/R)¹/²

This corresponds to option A: (GM/R)¹/².