If the mass of the planet is double the mass of earth and radius is half the radius of earth calculate value of gravity on the planet plz very urgent
Answers
Answered by
1
Let's first look at the equation for the force of gravity:
Fg=Gm1m2r2
which is often simplified for working with objects on the surface of the Earth (since we know the gravitational constant and the mass of the Earth) to
Fg=Mr2
where M is the mass experiencing Earth's gravity.
So what happens when we double the mass of the Earth and reduce its radius to 1/2? Let's multiply m1 by 2 and substitute in 12r for r. So first start with the full equation:
Fg=Gm1m2r2
then make the substitutions:
Fg=G(2m1)m2(12r)2
Fg=G(2m1)m214r
So the numerator increases linearly (×2 ) but the denominator reduces by an exponential - in this case (×4 ).
The force of gravity on Earth is roughly 9.8ms2but on this other planet, it would be:
9.8ms2⋅2⋅4=78.4ms2
Fg=Gm1m2r2
which is often simplified for working with objects on the surface of the Earth (since we know the gravitational constant and the mass of the Earth) to
Fg=Mr2
where M is the mass experiencing Earth's gravity.
So what happens when we double the mass of the Earth and reduce its radius to 1/2? Let's multiply m1 by 2 and substitute in 12r for r. So first start with the full equation:
Fg=Gm1m2r2
then make the substitutions:
Fg=G(2m1)m2(12r)2
Fg=G(2m1)m214r
So the numerator increases linearly (×2 ) but the denominator reduces by an exponential - in this case (×4 ).
The force of gravity on Earth is roughly 9.8ms2but on this other planet, it would be:
9.8ms2⋅2⋅4=78.4ms2
Similar questions