Show that weight of the body on moon is 1/6 times its weight on earth.

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Solution

$W_{e} = G \frac{M_{e} m}{{R_{m}}^{2}}$

Weight of the object on the moon is
$W_{m} = G \frac{M_{m} m}{{R_{m}}^{2}}$

So, the ratio of object of weight on moon to weight on earth is.
$\begin{matrix} \frac{W_{m}}{W_{e}} = \frac{G M_{m} m}{{R_{m}}^{2}} \times \frac{{R_{e}}^{2}}{G M_{e} m} \Rightarrow \frac{W_{m}}{W_{e}} = \frac{M_{m}}{M_{e}} \times {(\frac{R_{e}}{R_{m}})}^{2} = \frac{M_{m}}{100 M_{m}} \times {(\frac{4 R_{m}}{R_{m}})}^{2} = \frac{16}{100} = \frac{1}{6} \end{matrix}$

Therefore, the weight of an object on the moon is about $\frac{1}{6}$ of its weight on the earth.

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Question 95

The weight of an object on Moon is $\frac{1}{6}$ of its weight on Earth. If an object weighs $5 \frac{3}{5}$ kg on Earth. How much would it weigh on the Moon?

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Show that weight of the body on moon is 1/6 times its weight on earth.

We=GMemRm2Weight of the object on the moon isWm=GMmmRm2So, the ratio of object of weight on moon to weight on earth is.WmWe=GMmmRm2×Re2GMem⇒WmWe=MmMe×(ReRm)2=Mm100Mm×(4RmRm)2=16100=16Therefore, the weight of an object on the moon is about 16 of its weight on the earth.