Question

Force on a 1 kg mass on earth of radius R is 10 N. Then the force on a satellite revolving around the earth in the mean orbital radius $\dfrac{3R}{2}$ will be (mass of satellite is 100 kg).
A.) $4.44\times {{10}^{2}}N$
B.) 500N
C.) $3.33\times {{10}^{2}}N$
D.) $6.66\times {{10}^{2}}N$

Answer 1

Hint:The Force of gravity is a two-body force. This force always acts when two bodies having a mass interact to each other over a certain distance. It includes a Gravitational Constant (G) having the value $6.674\times {{10}^{-11}}N{{m}^{2}}K{{g}^{-2}}$. This force doesn’t require any medium, it also acts in a vacuum like the force of gravity the sun acts on earth.

Formula used:
$F=G\dfrac{Mm}{{{R}^{2}}}$

Complete Step by step solution:
We have been given the mass of a body and the distance and the force acting on it.
We have m=1Kg
Distance = R
Force= 10N
Where N stands for newton.

Applying the formula $F=G\dfrac{Mm}{{{R}^{2}}}$
Where M = Mass of earth
m = Mass of body
G= Gravitational constant
R = Distance of separation

Putting all the values we get,
So, we have $10=G\dfrac{M(1Kg)}{{{R}^{2}}}$
Or $10=G\dfrac{M}{{{R}^{2}}}$

Now the second thing we have given is that a satellite of mass 100Kg is revolving at a distance $\dfrac{3R}{2}$

So again, putting the values in the formula of gravitational force we get,
${{F}_{s}}=G\dfrac{Mm}{{{R}^{2}}}$
Where $F{}_{s}$ is the gravitational force between earth and the satellite.
${{F}_{s}}=G\dfrac{M(100Kg)}{{{(\dfrac{3R}{2})}^{2}}}$
${{F}_{s}}=G\dfrac{100M}{\dfrac{9{{R}^{2}}}{4}}$
${{F}_{s}}=G\dfrac{400M}{9{{R}^{2}}}$

But we know that $G\dfrac{M}{{{R}^{2}}}=10N$
Putting this value in above equation we get,
${{F}_{s}}=10\times (\dfrac{400}{9})$
${{F}_{s}}=444.44N$
Or ${{F}_{s}}=4.44\times {{10}^{2}}N$

Hence, we can conclude that option (A) is the correct answer.

Note:
Gravitational force is the weakest force in all of the four fundamental forces and the strong nuclear force is the strongest force in all of the fundamental forces. Gravitational force is a long-range force and it does not require any medium to act on anybody. The best example of this is the gravitational force between the sun and the earth.