Acceleration due to gravity-

The correct answer is option 1) i.e. increases with increase in latitude

CONCEPT:

• Law of Universal Gravitation: It states that all objects attract each other with a force that is proportional to the masses of two objects and inversely proportional to the square of the distance that separates their centres.

It is given mathematically as follows:

\(F = \frac{Gm_1m_2}{R^2}\)

Where m1 and m2 are the mass of two objects, G is the gravitational constant and R is the distance between their centres.

• From the Law of Universal Gravitation, the gravitational force acting on an object of mass m placed on the surface of Earth is:

\(F = \frac{GMm}{R^2}\)

Where R is the radius of the earth. 

From Newton's second law, F = ma = mg

\(⇒ mg =\frac{GMm}{R^2}\)

⇒ Acceleration due to gravity, \(g =\frac{GM}{R^2}\)

EXPLANATION:

• The latitude of a point is the angle between the equatorial plane and line joining that point to the centre of the earth.
• The latitude of the equator is 0^∘ and the latitude of poles is 90^∘. 
• We know that the earth is not a perfect sphere, but it is bulged outwards towards the equator.

From the relation \(g =\frac{GM}{R^2}\), the value of R is greater at the equator than at the poles.

• Hence, the acceleration due to gravity increases towards the poles.
• So, as we move from the equator to the poles, the latitude increases and the acceleration due to gravity increases.
• Thus, acceleration due to gravity increases with an increase in latitude.