Question

Gravitational force on the surface of the moon is only $\frac{1}{6}$ as strong as gravitational force on the earth. What is the weight in the newton’s of a $10kg$ object on the moon and on the earth?

Answer 1

Step 1: Given data

The gravitational force on the surface of the moon is only $\frac{1}{6}$ as strong as the gravitational force on the earth because the mass of the moon is $\frac{1}{6}$ the mass of the Earth.

Weight is a force that acts at all times on all objects near Earth. The Earth pulls on all objects with a force of gravity downward toward the center of the Earth.

Acceleration due to earth’s gravity

Object’s mass, $m=10kg$

Mass of the Moon, $m_m$

Given, $m_m=\frac{1}{6}{m}_e$

Step 2: Definition of Gravitational force.

The force of attraction between any two bodies is proportional to the product of their masses and inversely proportional to the square of their distance. The acceleration due to gravity on Earth is therefore,

$g_e=\frac{G{m}_e}{r^2}$

$W_e=g_{e}m$

Here $G$ is the Universal Gravitational constant, $m_e$is mass of the Earth, $r$ is the distance of the object from the Earth, $W_e$ weight of the object on Earth and $m$ is the mass of the object and $g_e$ is assumed to be $9.8m/s^2$

Step 3: Gravitation on the surface of the moon.

Therefore, acceleration due to gravitation on the moon,

$$\begin{gathered} g_m=\frac{G{m}_m}{r^2} \\ {g}_m=\frac{1}{6}\times \frac{G{m}_e}{r^2} \\ {g}_m=\frac{1}{6}{g}_e \end{gathered}$$

Weight of the object on Earth, $W_e=g_{e}m=9.8\times 10=98N$

Weight of the object on the moon,

$$\begin{gathered} W_m=g_{m}m \\ {W}_m=\frac{1}{6}\left(g_{e}m\right) \\ {W}_m=\frac{1}{6}{W}_e \\ {W}_m=\frac{1}{6}\times 98=16.34N \end{gathered}$$

Hence, the weight of the object on Earth is $98N$ and on the moon it is$16.34N$.