Question

find the value of acceleration due to gravity on planet having mass two times and radius 1/4 times than that of earth​

Answer 1

The mass increases linearly but radius decreases exponentially, so the result is 
9.8ms2⋅2⋅4=78.4ms2

Explanation:

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