Show that the weight of an object on the moon is $1 / 6 t h$ its weight on the earth. Given that the mass of the earth is $100$ times the mass of the moon and its radius $4$ times that of the moon.

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Solution

Step1- Assuming the data
Let,
Mass of moon $m = \frac{M}{100}$
Mass of the earth $= M$
Radius of moon $r = \frac{R}{4}$
Radius of the earth $= R$
Step2- Solution
$g_{e a r t h = G M / R^{2} . . . . . . . . . . . . . (1)} g_{m o o n = G m / r^{2} . . . . . . . . . . . . . (2)} w h e r e, m = M / 100 r = R / 4 E q u a t i o n 2 b e c o m e s g_{m o o n =} (G M / 100) / {(R / 4)}^{2} . . . . . . . . . . . (3) o n d i v i d i n g e q u a t i o n (1) a n d (3) w e g e t \frac{g_{e a r t h}}{g_{m o o n}} = \frac{16}{100}$
Step3- Conclusion
Hence 'g' on earth = $\frac{1}{6}$ 'g' on moon
As a result weight on the moon of a body is one-sixth times the weight of the body on the earth.

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