Question

What will the weight of a body of mass 40kg on a planet with mass twice of earth and radius 4 times of earth?

Answer 1

see the above image...

Answer 2

As we know that ,the accleration due to gravity of any planet is directly proportional to the mass of the planet and inversely proportional to the square of the radius.

As, in the case of earth we have , g

g = G.Me/Re^2

where G is universal gravitational const.

Me is mass of the earth (planet)

Re is the radius of the earth (planet).

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We have,

mass of planet, Mp = 2×Me

radius of the planet, Rp = 4×Re

so, accleration due to gravity of that planet

gp = G.Mp/Rp^2

or, gp = G.(2Me)/(4Re)^2

or, gp = 2/16 G.Me/Re^2


or, gp = 1/8 g________{as g= G.Me/Re^2}

As, g = 9.81 m/s^2

so, gp = 9.81/8 m/s^2 = 1.22625 m/s^2

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We have mass of body m= 40 kg

As we know that weight is given by

W = mass × acceleration due to gravity of that planet

so, Wp = m × gp = 40kg × 1.22625m/s^2

or, Wp = 49.05 kgm/s^2 = 49.05 N.

So, weight on the planet will be approx. 49 N.