A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other object in sky and take acceleration due to gravity on the surface of the Earth and mars as 10m/s2 and 4m/s2 respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time.
(A)(c)✓ Correct
(B)(a)
(C)(b)
(D)(d)
Answer: (A)
Solution
At the start the passenger rests on Earth and weighs 100×10=1000 N; at the end the passenger rests on Mars and weighs 100×4=400 N. In between, the pulls of the two planets act in opposite directions and the field strength falls off with distance, so the weight decreases smoothly, becomes exactly zero at the neutral point where the two pulls cancel, and then grows again as Mars is approached. Weight is the magnitude of the gravitational force, so it can never take a negative value. The curve that fits is the one that leaves 1000 N, falls to touch zero once at an intermediate time, and then rises to 400 N.
JEE Main · 2021 · 20 Jul 2021 · Shift 1 · Single correct option