Question

A mass of 1 kg on earth weighs 1/6 kg on moon. The radius of the moon is 1.738×10^6m.The mass of the moon is

Answer 1

The mass of the moon is $7.38\times10^{22}\ kg$

Explanation:

Given that,

Mass on earth = 1 kg

Weight on moon $w=\dfrac{1}{6}\ kg$

Radius $r=1.738\times10^{6}\ m$

We need to calculate the gravity on moon

Using formula of gravity at moon

$g_{m}=\dfrac{g_{e}}{6}$

Put the value into the formula

$g_{m}=\dfrac{9.8}{6}$

$g_{m}=1.63\ m/s^2$

We need to calculate the mass of the moon

Using formula of gravitational force

$g_{m}=\dfrac{GM_{m}}{R_{m}^2}$

$M_{m}=\dfrac{g_{m}\times(R_{m})^2}{G}$

Put the value into the formula

$g_{m}=\dfrac{1.63\times(1.738\times10^{6})^2}{6.67\times10^{-11}}$

$M_{m}=7.38\times10^{22}\ kg$

Hence, The mass of the moon is $7.38\times10^{22}\ kg$

Learn more :

Topic : gravitational force

https://brainly.in/question/12362681