Question

Calculate the acceleration due to gravity on the surface of the moon if the mass of the moon is $7.36\times {10}^{22}kg$and the radius is$1740km$. What will be the weight of a body of mass $10kg$ on the moon? Assume the value of $G$ $\left(G=6.67\times {10}^{-11}\frac{N{m}^2}{kg}\right)$.

Answer 1

Step 1: Given data,

1. Mass of the moon =$7.4\times {10}^{22}kg$
2. The radius of the moon $=1740km$
3. Gravitational constant $G=6.67\times {10}^{-11}\frac{N{m}^2}{kg}$

Step 2: Calculating the acceleration due to gravity on the surface of the moon.

The acceleration due to gravity on the surface of the moon can be calculated by using the formula

$g=\frac{GM}{R^2}$.

Here, $g$ is the acceleration due to gravity, $G$ is the gravitational constant, $M$is the mass of the earth, $R$is the radius of the earth.

$g=\frac{(6.67\times {10}^{-11})\times (7.4\times {10}^{22})}{{(1.74\times {10}^6)}^2}$

$g=\frac{6.67\times 7.4}{{(1.74)}^2}\times {10}^{-11+22-12}$

$g=\frac{6.67\times 7.4}{{(1.74)}^2}\times {10}^{-1}\frac{m}{s^2}$

$g=1.63\frac{m}{s^2}$

Step 3: Calculating the weight of the body

We know that,

$W=mg$

Here, $W$ is the weight of the body, $m$ is the mass of the body, $g$ is the acceleration due to gravity.

$W=10\times 1.63kg\frac{m}{s^2}$.

$W=16.3N$

Therefore, an object with a mass of $10kg$ has a weight on the moon of $16.3N$.