Question

If an object weighs 1300 N on earth's surface, what would be the approximate weight of an object on the surface of a planet with 8 times the mass of earth and 10 times the radius?

Answer 1

weight of an object is given by,

W = G*M*m/R^2

here, G = gravitational constant

M = mass of planet

m = mass of object

R = radius of planet

So, mass of object = m = W*R^2/(G*M)

Since, mass remain constant.

then, We*Re^2/(G*Me) = Wp*Rp^2/(G*Mp)

here, We = weight at earth = 1300 N

Wp = weight at planet = ??

Re = radius of earth

Rp = radius of planet

Me = mass of earth

Mp = mass of planet

Given, Mp/Me = 8

Rp/Re = 10

So, Wp = We*(Mp/Me)*(Re/Rp)^2

Wp = 1300*8*(1/10)^2

Wp = 104 N

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