Option 3 : \(\frac{1}{2}\)
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100 Questions 100 Marks 90 Mins
- 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 = $$\frac{G(8M_{earth})}{(2R_{earth})^{2}}$$
= $$2(\frac{GM_{earth}}{R_{earth}^{2}})$$
= $$2g$$
= $$20$$ $$ms^{-2}$$
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