The mass density of a spherical body is given by $\rho \left( r \right) = \frac{k}{r}$ for $r \leq R\,\,$ and $\rho \left( r \right) = 0\,$ for $r > R$ , where $r$ is the distance from the centre. The correct graph that describes qualitatively the acceleration, $a$, of a test particle as a function of $r$ is

Obtain general equation of gravitation force at distance $r$ from the centre of earth and derive the equation of acceleration due to gravity on the surface of earth.

The value of g on the earth's surface is $980\,cm/{\sec ^2}$. Its value at a height of $64 \,km$ from the earth's surface is …….. $cm/{\sec ^2}$

(Radius of the earth $R = 6400$ kilometers) 

The radii of two planets $A$ and $B$ are $R$ and $4 R$ and their densities are $\rho$ and $\rho / 3$ respectively. The ratio of acceleration due to gravity at their surfaces $\left(g_A: g_B\right)$ will be

The weight of an object in the coal mine, sea level, at the top of the mountain are ${W_1},\;{W_2}$ and ${W_3}$ respectively, then