The height at which the weight of a body becomes $1/16^{th}$, its weight on the surface of earth (radius $R$), is

Which of the following statements are true about acceleration due to gravity?

$(a)\,\,'g'$ decreases in moving away from the centre if $r > R$

$(b)\,\,'g'$ decreases in moving away from the centre if $r < R$

$(c)\,\,'g'$ is zero at the centre of earth

$(d)\,\,'g'$ decreases if earth stops rotating on its axis

Figure shows the variation of the gravitatioal acceleration $a_g$ of four planets with the radial distance $r$ from the centre ofthe planet for $r \ge $ radius of the planet. Plots $1$ and $2$ coincide for $r \ge {R_2}$ and plots $3$ and $4$ coincide for $r \ge {R_4}$ . The sequence of the planets in the descending order of their densities is

If $v_e$ is escape velocity and $v_0$ is orbital velocity of satellite for orbit close to the earth's surface. Then these are related by

A satellite in force free space sweeps stationary interplanetary dust at a rate of $\frac{d M}{d t}=\alpha v$ where $M$ is mass and $v$ is the speed of satellite and $\alpha$ is a constant. The acceleration of satellite is

The force of gravitation is