A satellite moves in a circular orbit of radius 4R round the earth. The acceleration of the satellite in terms of g is

Analyze the question: The satellite orbits at a distance of 4R from the Earth's centre (R is the Earth's radius). We need its acceleration, which is the gravitational field strength at that distance, expressed in terms of g.

Concept: Gravitational acceleration depends on distance from the Earth's centre:

This is the inverse square law. If the distance increases by a factor n, the acceleration decreases by a factor n².

Solution:

At the Earth's surface: $g = \dfrac{GM}{R^2}$

At the orbit, r = 4R:

Check on the options: C and D (4/g and 16/g) have the wrong dimensions, since acceleration cannot be written as a number divided by g. Also, the acceleration must decrease with distance, so it must be smaller than g. Option B (g/4) would only be right if the radius were 2R.

Answer: A, g/16

Exam tip: Remember "double the distance, quarter the pull; triple the distance, one-ninth." For any radius nR, the acceleration is g/n². Just square the multiplier and put it under g.