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

Weight of a body of mass $m$ decreases by $1\%$ when it is raised to height $h$ above  the Earth's surface. If the body is taken to a depth $h$ in a mine, then its weight will

Obtain an expression for the variation in effective gravitational acceleration $g'$ with latitude due to earth’s rotation.

Assuming the earth to be a sphere of uniform mass density, a body weighed $300 \mathrm{~N}$ on the surface of earth. How much it would weigh at $R / 4$ depth under surface of earth?

The mass and diameter of a planet have twice the value of the corresponding parameters of earth. Acceleration due to gravity on the surface of the planet is …….. $m/{\sec ^2}$.