Question

Dependence of intensity of gravitational field (e) of earth with distance (r) from centre of earth is correctly represented by

Answer 1

The graph is attached.


Intensity of gravitational field is also known as gravitational acceleration $\textbf{\textit{g}}$.

Now, Let

Earth's Radius = R
Earth's Mass = M
Universal Gravitational Constant = G

Also, r = Distance from center of Earth


 Now, the value of g is given by the following formulas. Their graph description is also given.



$\boxed{g = -\frac{GMr}{R^3} \, \, \, for \, \, r \ \textless \ R} \, \, \, \implies \text{Straight Line} \\ \\ \\ \boxed{g = -\frac{GM}{R^2} \, \, \, for \, \, r=R } \, \, \, \implies \text{Constant Value} \\ \\ \\ \boxed{g = -\frac{GM}{r^2} \, \, \, for \, \, r\ \textgreater \ R} \, \, \, \implies \text{Hyperbola}$

As we can see, 

For r<R, the value of g is directly proportional to R. So the graph is a straight line. 

g reaches a Maximum Value for  r = R



For r > R, the value of g is inversely proportional to $r^2$. So the graph is a decreasing hyperbola.

The graph is attached as an image.

Answer 2

Answer: gravitational field intensity is -ve

Explanation: