Question

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What effect will be on acceleration due to gravity if radius of the earth is decreased?

Answer 1

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✍️The acceleration due to gravity on the earth can change in various ways as the earth shrinks. If you look up at the rate of change of g with respect to decrease in R the radius of Earth, it will vary as 1/Radius of the old value ; so the acceleration due to gravity increases with reduction in radius.

✍️Mass does not affect the speed of falling objects, assuming there is only gravity acting on it. Both bullets will strike the ground at the same time. The horizontal force applied does not affect the downward motion of the bullets -- only gravity and friction (air resistance), which is the same for both bullets.

✍️The strength of the gravitational force between two objects depends on two factors, mass and distance. the force of gravity the masses exert on each other. ... increases, the force of gravity decreases......
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Answer 2

Acceleration due to gravity is denoted by the small g . Its value will change depending on the source of gravity and the mass of the object .

The formula for the acceleration due to gravity is :

$\mathtt{g=\dfrac{GMm}{R^2}}$

In the above formula G is the Universal Gravitational Constant which never ever changes its value . It will be the same at the centre of a super massive black hole , same in your bathroom or even at the centre of the Sun .

So the value of g will be independent of the value of G .

Now M is the mass of the Earth which will also not change unless in hypothetical situations .

m is the mass of the object which will also not change in the given case as we are not changing the mass of any object to compare with g .

So the thing which changes is R or the radius of the Earth .

Since the denominator of the fraction is changing , then the result will be just the opposite on the other side of the fraction .

In simple words ,

The acceleration due to gravity is inversely proportional to the square radius of the Earth .

EDIT : g ∝ 1/R² which expresses the relation .

Here g is inversely proportional to the R where the constant will be G × M × m .

Now if we decrease the radius of the Earth , then the acceleration due to gravity will increase by the square of the decrease of radius .