Show that the weight of an object on the moon is 1/6th its weight on the earth.

Given that the mass of the earth is 100 times the mass of the moon and its radius is 4 times

that of the moon.

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1/6th of its weight on the earth

2 times its weight on the earth

5 times its weight on the earth

1/3rd of its weight on the earth

answer is A.

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Detailed Solution

Step 1,
The weight of an object of mass m is,
W = mg
The acceleration due to gravity is ,
g=GMR2
Where M is the mass of the planet and ‘g’ we have to find and R is its radius.
Step 2,
For Moon,
Mm=7.36×1022 kg
Rm=1.74×106 m
So,
gm=GMmR2m
For earth,
Me=5.98×1024 kg
Re=6.37×106 m
So,
ge=GMeR2e
Step 3,
gmge=(MmR2e)(MeR2m)
Putting all the values we get,
gmge=7.36×1022×(6.37×106)25.98×1024×(1.74×106)2
gmge=0.165
ge=gm0.165
≈6gm
Therefore, the weight of an object on the moon is 1/6 of its weight on the earth.

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