Question

As we go from the equator to the poles, the value of g

1. Remains the same
2. Decreases
3. Increases
4. Decreases up to latitude of 45 degrees.

Answer 1

We all know that an object which is in a state of free fall is under the sole influence of gravity and the value of gravitational acceleration is given by $9.8m{s^{ - 2}}$. Here we also know the formula for the gravitational force which is given by Sir. Isaac Newton. Put the formula F = ma; where F = force, M = mass, a = Acceleration in the formula for gravitation and derive acceleration due to gravity.

Formula used: Formula for gravitational force:
$F = G\dfrac{{Mm}}{{{r^2}}}$;
Where:
F = force;
M = mass of object 1;
m = mass of object 2;
G = Gravitational Constant ($6.67 \times {10^{ - 11}}{m^3}k{g^{ - 1}}{s^{ - 2}}$);
r = distance between two objects;

Complete step-by-step answer:
Derive the gravitational acceleration and find out the relation between gravitational acceleration g and distance r.
The formula for gravitational force is given by:
$F = G\dfrac{{Mm}}{{{r^2}}}$;
Now, according to Newton’s 2nd law F=ma, put this value in the above equation,
$ma = G\dfrac{{Mm}}{{{r^2}}}$;
Both the masses are same so they will cancel each other out
$a = G\dfrac{M}{{{r^2}}}$;
$g = G\dfrac{M}{{{r^2}}}$; …(a = g)
Hence we have the formula for gravitational acceleration (g). Here we can see that there is an inverse relation between g and r. In other words for gravitational acceleration (g) is inversely proportional to the distance (r).

Final Answer: Option “3” is correct. As we go from the equator to the poles, r decreases and as established that there is an inverse relation between g and r, so as r decreases the value of g will increase.

Note: Here we need to note that Earth is not a perfect sphere; it is bulging at the equator, so the distance from the core of the Earth to the equator is more than the distance of the earth’s core to the poles. So as we move towards the pole the distance will decrease resulting in an increase in g.