A2 Daily A Level Physics question
In a tethered test near a small spherical moon (no atmosphere), a 1.0 kg package is moved very slowly by a winch from a distance R from the moon’s centre to 2R, and later from 2R to a point so far away the moon’s pull is negligible. Kinetic energy changes are negligible. Which statement must be true?
Answer
The correct answer is D.
Correct: D — The work needed from R to 2R equals the work from 2R to very far away; the field strength at 2R is one quarter of its value at R. A asserts less work in the first leg and a 1/r fall in g; in fact, the potential becomes less negative as 1/r, so the rise from R to 2R equals the remaining rise to zero, and g falls with the square of distance, not linearly. B has the correct 1/4 factor for g but wrongly claims more work is needed from R to 2R; the two legs require equal work because each covers half the total rise in potential from −(constant)/R to 0. C is right that the two works are equal but incorrectly states g halves rather than quarters when the distance is doubled. D combines both correct ideas: equal work in the two legs due to potential varying as 1/r (zero at infinity), and g at 2R is one quarter of g at R due to the inverse-square dependence.