Concept of weight

The weight of a person on a planet is $W = mg$ where $m$ is the mass of the person and $g$ is the local acceleration due to gravity.

Weight on Earth and Mars

Given: $m = 100\,\text{kg}$ $g_E = 10\,\text{m/s}^2$ $g_M = 4\,\text{m/s}^2$

So,

• On Earth: $W_E = 100 \times 10 = 1000\,\text{N}$
• On Mars: $W_M = 100 \times 4 = 400\,\text{N}$

What happens during the journey?

We are told to neglect all other celestial bodies except Earth and Mars.

• At the start, near Earth, the person’s weight is about $1000\,\text{N}$.
• As the spaceship moves away from Earth, Earth’s gravitational pull decreases, so weight decreases.
• Somewhere between Earth and Mars, the gravitational pulls of Earth and Mars can balance, so the net gravitational force becomes zero. Hence weight becomes zero at one instant.
• As the spaceship approaches Mars, Mars’ gravitational pull increases, so the weight increases again.
• Finally on Mars, the weight becomes $400\,\text{N}$.

Shape of the graph

Therefore, the graph of weight vs time should:

• start from a large value ($1000\,\text{N}$),
• decrease continuously,
• touch zero once,
• then increase,
• finally reach a smaller constant value ($400\,\text{N}$) on Mars.

So the correct curve is the one that starts high, dips to zero, then rises to a lower final value than the initial value.

Matching with options

From the given labels:

• Option A corresponds to figure $(b)$
• Option B corresponds to figure $(c)$
• Option C corresponds to figure $(d)$
• Option D corresponds to figure $(a)$

The required graph is figure $(c)$.

Final answer

Hence the correct option is: $\boxed{\text{B}}$