Question

An object weight $10\,N$ when measured on the surface of the earth. What would be its weight when measured on the surface of the moon?

Answer 1

The moon's mass is $\dfrac{1}{{100}}$ that of the earth, while its radius is $\dfrac{1}{4}$ that of the earth. As a result, the moon's gravitational attraction is about one-sixth that of Earth. The gravitational force of the moon is influenced by its mass and size. As a result, the weight of an object on the moon is $\dfrac{1}{6}$that of an object on Earth. The moon is significantly less massive and has a different radius $\left( R \right)$ than the Earth.

Complete step by step answer:
From the given question, we know that the weight of the body on earth is,
${W_e} = 10kg$
We know that a body's weight on Earth equals the product of its mass and its acceleration due to gravity (gravitational force on earth).
${W_e} = m{g_e}$
We know that the acceleration due to gravity (the earth's gravitational force) equals $9.8m \cdot {s^{ - 2}}$
Because we know that mass is a fixed quantity. It is not affected by its location.
Substitute the given value in the above equation, we get,
$10 = m{g_e} \\\ \Rightarrow m = \dfrac{{10}}{{9.8}}kg \\\$
The acceleration caused by the gravitational force on the moon is around six times that caused by the gravitational force on the earth.
${g_m} = 6{g_e}$
The weight of a body on the moon is calculated as follows:
${W_m} = m{g_m}$
Rewrite the above equation,
${W_m} = m\left( {\dfrac{6}{{{g_e}}}} \right)$
When the values and expressions in the above equation are substituted, we get:
${W_m} = \dfrac{{10}}{{9.8}} \times \left( {\dfrac{{9.8}}{6}} \right) \\\ \therefore {W_m} = \dfrac{{10}}{6} = 1.67N \\\$
Hence, the weight on the moon is $1.67\,N$.

Note: Always keep in mind that body mass is a property of matter that is a continuous quantity that is independent of its location. Mass can't be zero, and it only has one magnitude, thus it's a straightforward quantity. $kg$ is the SI unit for it. Weight, on the other hand, is the product of mass and gravitational acceleration. It is dependent on the location. The weight of the body is different between planets or Satellites since each planet has its own gravitational force. It might be nil.