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
$\frac{-\alpha v^{2}}{M}$
$-\alpha v^{2}$
$\frac{-2 \alpha v^{2}}{M}$
$\frac{-\alpha v^{2}}{2 M}$
Assume that a tunnel is dug through earth from North pole to south pole and that the earth is a non-rotating, uniform sphere of density $\rho $. The gravitational force on a particle of mass $m$ dropped into the tunnel when it reaches a distance $r$ from the centre of earth is
The variation of acceleration due to gravity $ ( g )$ with distance $(r)$ from the center of the earth is correctly represented by ... (Given $R =$ radius of earth)
The orbit of geostationary satellite is circular, the time period of satellite depends on $(i)$ mass of the satellite $(ii)$ mass of the earth $(iii)$ radius of the orbit $(iv)$ height of the satellite from the surface of the earth
When a body is taken from pole to the equator its weight
A body weighs $700\,gm\,wt.$ on the surface of the earth. How much will it weigh on the surface of a planet whose mass is $\frac {1}{7}$ and radius half of that of the earth ....... $gm\, wt$