Question

an object weighs 10N on surface of earth what will be its weight on planet if its mass is one tenth that of Me and radius is one half of Re

Answer 1

Given

Weight of object : 10N

Mass of planet P : Me/10

Radius of planet P : Re/2

Since we know that

F = $\frac{GMe.m}{Re^{2} }$

Then , gravitational force on planet P

F' = $\frac{GMp.m}{Rp^{2} }$

Mp = Me/10

Rp = Re/2

Putting the values

F' = (G Me/10 . m) / (Re/2)^2

Simplifying the above eqn. , we get

F' = $\frac{2}{5}$ $\frac{GMe.m}{Re^{2} }$

and

F' =  $\frac{2}{5}$ F

F' =  $\frac{2}{5}$ * 10

F' = 4N

Therefore , weight of the body on planet P = 4N

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I hope you understand.