Question

A body weighs 5.6 kg wt on the surface
of the Earth. How much will be its
weight on a planet whose mass is 7 times
the mass of the Earth and radius twice
that of the Earth's radius.​

Answer 1

its simple you only have to multiply the mass of earth by 7 and after that divide the given answer by 5.6

Answer 2

Given :

• Force/weight of the body on earth = 5.6 kg wt

• Mass of the planet = 7 × Mass of Earth

• Radius of the planet = 2 \times Radius of the Earth

To find :

Force of Gravitation on that planet.

Solution :

Let the mass of Earth be m kg.

Let the distance between the two bodies be r m.

Now , using the formula for Gravitational force of an body and substituting the values in it, we get :

$\bf{F = G\dfrac{m_{1}{m_{2}}}{r^{2}}}$

Where :-

• F = Gravitational force
• m = Mass
• r = Distance between the two bodies.

$:\implies \bf{F = G\dfrac{m\:m_{2}}{r^{2}}}$ [Eq.1]

Force of Gravitation between the two bodies when mass of Earth is 7 times and the distance is doubled.

$:\implies \bf{F' = G\dfrac{7m\:m_{2}}{(2r)^{2}}}$

$:\implies \bf{F' = G\dfrac{7m\:m_{2}}{4r^{2}}}$ [Eq.2]

To find the Gravitational force on the planet :-

To find the Force of Gravitation first we have to find the relation between the planet and the Earth.

By dividing their force of Gravitation we can find the value of force of Gravitation of the planet in terms of force of Gravitation of the Earth.

And then by Substituting the value of force of Gravitation of earth in the relation, we can find the required value !!

Now , dividing Equation (i) from Equation (ii) , we get :

$:\implies \bf{\dfrac{F'}{F} = \dfrac{G\dfrac{7m\:m_{2}}{4r^{2}}}{G\dfrac{m\:m_{2}}{r^{2}}}}$

$:\implies \bf{\dfrac{F'}{F} = G\dfrac{7m\:m_{2}}{4r^{2}} \times G\dfrac{r^{2}}{mm_{2}}}$

$:\implies \bf{\dfrac{F'}{F} = \dfrac{7}{4}}$

Now , by substituting the value of F in the Equation , we get :

$:\implies \bf{\dfrac{F'}{5.6} = \dfrac{7}{4}}$

$:\implies \bf{F' = \dfrac{7}{4} \times 5.6}$

$:\implies \bf{F' = 7 \times 1.4}$

$:\implies \bf{F' = 9.8}$

$\boxed{\therefore \bf{Force\:on\:the\:body\:(F') = 9.8\:kg wt}}$

Hence, the Gravitational force on the planet will be 9.8 kg wt.