What will be the acceleration due to gravity at a planet whose mass is it times the mass of the Earth and whose radius is twice that of the earth?

Option 3 : $\frac{1}{2}$

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Consider the mass of earth as ‘M’ and radius of earth ‘R’.
Now we consider a planet twice the mass and radius of earth as 2M and 2R.
We know the earth g = GM/R2 i.e. is g$\; \propto \frac{M}{{{R^2}}}$ where G is Universal Gravitational Constant.
Let g1 is acceleration due to gravity on earth and g2 is acceleration due to the gravity of another planet.
So g2/g1 = (2M/M) × (R/2R)2
c
According due to gravity on surface of planet is n times of earth we get g2 = g1(n)
Hence, the value n is ½.

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What will be the acceleration due to gravity at a planet whose mass is eight times the mass of the earth and whose radius is twice that of the earth? ($$g$$ on earth is $$10{ms}^{-2}$$) Acceleration due to gravity = $$\frac{GM}{R^{2}}$$

For the given planet,

$$M$$ = $$8M_{earth}$$

$$R$$ = $$2R_{earth}$$

Therefore , acceleration due to gravity on the planet = $$\frac{G(8M_{earth})}{(2R_{earth})^{2}}$$

= $$2(\frac{GM_{earth}}{R_{earth}^{2}})$$

= $$2g$$

= $$20$$ $$ms^{-2}$$