Select the correct option of the following:

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Both (A) and (R) are true and (R) is the correct explanation of (A)

Both (A) and (R) are true but (R) is not the correct explanation of (A)

(A) is true but (R) is false

Both (A) and (R) are false

answer is B.

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Detailed Solution

The gravitational force between an object on the earth and the earth can be given as:
$F = \frac{G M m}{R^{2}}$
Where M is the mass of the earth, m is the mass of the object, R is the radius of the earth and G is the universal gravitation constant and has a value of $6.67 X 10^{- 11} N m^{2} / k g^{2}$ . However 'g' is the acceleration due to gravity and can be given as:

$g = \frac{G M}{R^{2}}$

We can see that 'g' depends on the Mass and Radius of the planet.
Therefore, it can have a different value at different places like the poles and equator where the radius of the earth is slightly different. The value of 'g' at the pole is higher than the equator as the radius is smaller than the radius at the equator.
The value of 'g' will be different on different planets due to differences in mass and radius.

Therefore, we can say that both statements are correct. However, the constant value of the universal gravitation constant is not the reason for 'g' having different values at different places.
Hence option B is the correct answer.

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