g_moon = g_earth/6. Weight on moon = 60 × 10/6 = 100 N. Why g is lower on the moon.

What is the Weight of 60 kg Person on the Moon? — Gravity Comparison

Question

A person weighs 60 kg on Earth. What will be their weight on the Moon?

(NCERT Class 9, Chapter 10 — Gravitation)

Solution — Step by Step

Weight is not the same as mass. Mass (60 kg) stays the same everywhere in the universe — it’s the amount of matter. Weight is the force of gravity acting on that mass, and it changes depending on where you are.

W = mg

where $g$ is the acceleration due to gravity at that location.

On Earth, $g_{Earth} = 9.8 \, \text{m/s}^2$ , which we round to $10 \, \text{m/s}^2$ for board exams.

The Moon’s gravity is weaker because it has less mass and a smaller radius. The standard result you must remember:

g_{Moon} = \frac{g_{Earth}}{6} = \frac{10}{6} \approx 1.67 \, \text{m/s}^2

W_{Earth} = m \times g_{Earth} = 60 \times 10 = 600 \, \text{N}

This confirms our calculation path — if you get 600 N here, you’re set up correctly.

W_{Moon} = m \times g_{Moon} = 60 \times \frac{10}{6} = 60 \times 1.67 = 100 \, \text{N}

Weight on Moon = 100 N

The person’s mass remains 60 kg on the Moon, but their weight drops to one-sixth of what it is on Earth.

Why This Works

The Moon is much smaller and less massive than Earth. According to Newton’s law of gravitation, the gravitational force depends on the mass of the planet and the distance from its centre. The Moon’s mass is about 81 times less than Earth’s, and its radius is about 3.7 times smaller — these two factors combine to give a surface gravity roughly one-sixth of Earth’s.

This is why astronauts on the Moon can jump much higher and objects feel dramatically lighter. The amount of matter (mass) hasn’t changed — only the gravitational pull acting on it.

Quick formula for Moon problems: Whatever the weight on Earth, divide by 6 to get Moon weight. Conversely, multiply Moon weight by 6 to get Earth weight. This ratio is fixed and direct.

Alternative Method

Instead of using $g$ values directly, use the ratio approach:

\frac{W_{Moon}}{W_{Earth}} = \frac{g_{Moon}}{g_{Earth}} = \frac{1}{6}

So:

W_{Moon} = \frac{W_{Earth}}{6} = \frac{600}{6} = 100 \, \text{N}

This method is faster in exams — you don’t need to recall the exact value of $g_{Moon}$ , just the ratio $\frac{1}{6}$ .

If the question gives weight on Moon and asks for weight on Earth, just multiply by 6. Same formula, reversed.

Common Mistake

The mass-weight confusion. Many students write “the person’s mass on the Moon is 10 kg” — this is wrong. Mass never changes. Only weight changes with location. If asked “what is the mass of the person on the Moon?”, the answer is still 60 kg, not 10 kg. The examiner specifically tests this distinction in CBSE boards.

A second trap: some students use $g = 9.8 \, \text{m/s}^2$ and then get a messy decimal answer. For CBSE Class 9, always use $g = 10 \, \text{m/s}^2$ unless the question specifically asks otherwise — it keeps the numbers clean and avoids rounding errors.

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

Try These Next