Gravitation - Mass and Weight

Mass of an object is $10 \text{ kg}$. What is its weight on the Earth?

$W = m \times g$ $W = 10 \text{ kg} \times 9.8 \text{ m/s}^2 = 98 \text{ N}$

To find the weight, we multiply the mass of the object by the acceleration due to gravity on Earth ($g \approx 9.8 \text{ m/s}^2$).

An object weighs $60 \text{ N}$ when measured on the surface of the Earth. What would be its weight when measured on the surface of the Moon?

$W_{moon} = \frac{1}{6} \times W_{earth}$ $W_{moon} = \frac{1}{6} \times 60 \text{ N} = 10 \text{ N}$

The acceleration due to gravity on the Moon is $\frac{1}{6}^{th}$ of that on the Earth, so the weight of any object becomes $\frac{1}{6}$ of its weight on Earth.

If the mass of a body is $30 \text{ kg}$ on Earth, what will be its mass and weight on the Moon? (Take $g = 9.8 \text{ m/s}^2$)

Mass on Moon $= 30 \text{ kg}$. Weight on Moon: $W_{moon} = \frac{1}{6} \times (m \times g_{earth})$ $W_{moon} = \frac{1}{6} \times (30 \text{ kg} \times 9.8 \text{ m/s}^2) = 49 \text{ N}$

Mass remains constant everywhere in the universe. However, weight changes based on the local acceleration due to gravity. The weight on the Moon is calculated by taking one-sixth of the weight on Earth.