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Why is the Weight of an Object on the Moon 1/6th Its Weight on the Earth? - Science

Why is the weight of an object on the moon 1/6th its weight on the earth?

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Solution

Let ME be the mass of the Earth and m be an object on the surface of the Earth. Let RE be the radius of the Earth. According to the universal law of gravitation, weight WE of the object on the surface of the Earth is given by,

`W_E=(GM_Em)/R_E^2`

Let MM and Rbe the mass and radius of the moon. Then, according to the universal law of gravitation, weight WM of the object on the surface of the moon is given by:-

`W_E=(GM_Mm)/R_M^2`

`W_M/W_E=(M_MR_E^2)/(M_ER_M^2)`

`"Where, "M_E=5.98xx10^24kg," "M_M=7.36xx10^22kg`

`R_E=6.4xx10^6m," "R_M=1.74xx10^6m`

`thereforeW_M/W_E=(7.36xx10^22xx(6.37xx10^6)^2)/(5.98xx10^24xx(1.74xx10^6)^2)=0.165approx1/6`

Therefore, weight of an object on the moon is `1/6` of its weight on the Earth.

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APPEARS IN

NCERT Class 9 Science Textbook
Chapter 10 Gravitation
Q 2 | Page 138
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