A research satellite of mass $200 \,kg$ circles the earth in an orbit of average radius $3\,R/2$ where $ R$ is the radius of the earth. Assuming the gravitational pull on a mass of $1 \,kg$ on the earth’s surface to be $10 \,N$, the pull on the satellite will be ........ $N$. 

The angular velocity of the earth with which it has to rotate so that acceleration due to gravity on $60^o$ latitude becomes zero is (Radius of earth $= 6400\, km$. At the poles $g = 10\,m{s^{ - 2}})$

A simple pendulum has a time period ${T_1}$ when on the earth’s surface and ${T_2}$ when taken to a height $R$ above the earth’s surface, where $R$ is the radius of the earth. The value of ${T_2}/{T_1}$ is

The variation of acceleration due to gravity $g$ with distance $d$ from centre of the earth is best represented by ($R =$ Earth's radius)

A $90 \mathrm{~kg}$ body placed at $2 \mathrm{R}$ distance from surface of earth experiences gravitational pull of : ( $\mathrm{R}=$ Radius of earth, $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )

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