Question

Suppose that the radius of the earth becomes twice of its original radius without any change in is mass. Then what will happen to your weight?

July 30, 2024

Answer

We know that F = ${𝐺𝑀𝑚 \over 𝑟^2}$ as weight of a body is the force with which a body is attracted towards the earth,

∴ W = ${𝐺𝑀𝑚 \over 𝑟^2}$

If the radius of the earth becomes twice of its original radius, then

W = ${𝐺𝑀𝑚 \over (2𝑟^2)}$

= ${𝐺𝑀𝑚 \over 4𝑟^2}$ = ${𝑊 \over 4}$

i.e., weight will be reduced to one-fourth of the original.

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