Question 6
The acceleration due to gravity on the surface of earth is $$g$$. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :
Solution
The acceleration due to gravity on the surface of Earth is:
$$g = \frac{GM}{R^2}$$
If the diameter is halved, the radius becomes $$R' = R/2$$.
$$g' = \frac{GM}{(R/2)^2} = \frac{GM}{R^2/4} = \frac{4GM}{R^2} = 4g$$
The answer is $$4g$$, which corresponds to Option (4).
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