Question

prove that :
weight of the object on the moon = (1/6)×its weight on the earth​

Answer 1

We are asked to prove that, weight of the object on the moon = (1/6) × its weight on the earth.

~ Firstly let us revise the below mentioned criteria properly to solve this question!

Celestial bodies: Moon and earth respectively.

Mass of Moon and earth respectively: 7.36 × 10²² and 5.98 × 10²⁴

Radius of Moon and Earth respectively = 1.74 × 10⁶ and 6.37 × 10⁶

Now let us assume that the mass of an object becames m. Let's the weight of the similar object on moon becames ${\sf{W_m}}$ and let let mass of moom becames ${\sf{M_m}}$ and let's the radius of moon becames ${\sf{R_m}}$ Now let the weight of same object on earth becames ${\sf{W_e}}$ Let the mass of earth is ${\sf{M}}$ and the radius as ${\sf{R}}$

Firstly let equation first as the formula of gravity that is given below:

${\small{\underline{\boxed{\sf{g \: = G\dfrac{M}{R^2} \: \dots \: Eq^n \: 1}}}}}$

Now according to the universal law of gravitation the weight of the object on the surface of moon will be

${\small{\underline{\boxed{\sf{W_m \: = G\dfrac{M_m \times m}{R^2_m} \: \dots \: Eq^n \: 2}}}}}$

Now combining equation first and second we get the following results:

$:\implies \sf W_e \: = G\dfrac{Mm}{R^2} \: \dots \: Eq^3$

Now we have to use our creteria and have to imply values from this in equation third, let's imply and further solve!

$:\implies \sf W_m \: = G\dfrac{7.36 \times 10^{22} \times m}{(1.74 \times 10^6)}^2 \\ \\ :\implies \sf W_m \: = 2.431 \times 10^{10} \: \dots \: Eq^4 \: (a) \\ \\ :\implies \sf W_e \: = 1.474 \times 10^{11} \: \dots \: Eq^4 \: (b)$

Now we have to divide Equation 4 (a) with Equation 4 (b) and further solve!

$:\implies \sf \dfrac{W_m}{W_e} \: = \dfrac{2.431 \times 10^{10}}{1.474 \times 10^{11}} \\ \\ :\implies \sf \dfrac{W_m}{W_e} \: = 0.165 \: \approx \: \dfrac{1}{6} \\ \\ {\pmb{\sf{Henceforth, \: proved!}}}$

Therefore, proved that weight of the object on the moon = (1/6) × its weight on the earth.

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Important while solving this question: Don't forget law of exponents. Use them carefully, any single mistake will led to wrong way to answer.