A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as 10 m/s² and 4 m/s² respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time.

Solution

Physics sir · 4 steps

Earth and Mars pull in opposite directions, so somewhere on the way the weight must drop to exactly zero.

1. End points. On Earth the weight is 100 × 10 = 1000 N. On Mars it is 100 × 4 = 400 N. Every curve starts at A and ends at B, so the ends alone cannot decide the answer.
2. Two opposing pulls. In between, Earth pulls the passenger back and Mars pulls him forward. The weight is the size of the net pull, and each pull varies as 1/r², so the graph cannot be a straight line.

   W = | (GM_E m)/x² - (GM_M m)/(d - x)² |

3. Null point. Leaving Earth, the Earth term shrinks and the Mars term grows. At one point the two are equal and W = 0. Past that point Mars wins and W rises to 400 N. Weight is a magnitude, so it touches zero but never goes below it.

   Option	Curve	Shape	Fits?
   (a)	(b)	falls smoothly, never reaches zero	no
   (b)	(c)	falls to exactly zero, then rises to 400 N	yes
   (c)	(d)	dips below zero	no
   (d)	(a)	straight line	no

4. So. Only curve (c) falls to zero at the null point and then climbs to 400 N. That is option (b).

The idea to keep. Between two planets the gravitational pulls oppose each other, so the net weight always passes through zero at the null point. A magnitude touches zero but never goes negative.

Answer from the NTA final answer key. Solution by PrepWiser.