Question

2. An object experiences an acceleration, g, when it is on the surface of a planet of radius R. What will be
the acceleration on the object after it has been moved to a distance of 4R from the center of the planet?
A) 16g
B) 4g
C) 1/4 g
D) 1/16g

Answer 1

The new acceleration of gravity is D) 1/16 g

Explanation:

The magnitude of the acceleration of gravity in the gravitational field of a planet is given by

$g=\frac{GM}{r^2}$

where

G is the gravitational constant

M is the mass of the planet

r is the distance of the object from the centre of the planet

In this problem, the acceleration of gravity g on the surface of the planet (when r=R) is

$g=\frac{GM}{R^2}$

Then the object is moved to a distance of

r' = 4R

Substituting into the original equation, we can find what is the new acceleration of gravity:

$g'=\frac{GM}{(4R)^2}=\frac{1}{16}(\frac{GM}{R^2})=\frac{1}{16}g$

So, the acceleration of gravity has decreased by a factor 16.

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