Question

The escape velocity for a planet is ve. a tunnel is dug along a diameter of the planet and asmall boy is dropped into it at the surface. when the body reaches the center of the planet,its speed will be

A. ve
B. ve/√2
C. ve/2
D. Zero

Answer 1

The speed of the boy at the center of the planet will be zero as the gravitational forces from all sides are equal and cancel each other out at that point.

Step-by-step explanation:

When a small boy is dropped into a tunnel going through the diameter of a planet, the concept of escape velocity is not directly relevant to the speed the boy will reach at the center of the planet. Escape velocity is the minimum initial velocity that an object must have to escape the gravitation of a celestial body without further propulsion. However, this situation relates to the boy's velocity influenced by the planet's gravity as he falls through the tunnel.

As the boy descends into the tunnel, the gravitational force, and thus the acceleration, decreases because the amount of the planet's mass that is exerting a gravitational pull on him becomes less symmetrically distributed around him. At the center of the planet, the gravitational force from all sides is equal and cancels out, so the boy no longer experiences a net gravitational force, and hence his speed will be zero at that point, assuming no other forces such as air resistance are acting on him.