In order to make the effective acceleration due to gravity equal to zero at the equator, the angular velocity of rotation of the earth about its axis should be $(g = 10\,m{s^{ - 2}}$ and radius of earth is $6400 \,kms)$
$0\,\;rad\,{\sec ^{ - 1}}$
$\frac{1}{{800}}rad\,se{c^{ - 1}}$
$\frac{1}{{80}}rad\,se{c^{ - 1}}$
$\frac{1}{8}rad\,se{c^{ - 1}}$
Two planets move around the sun. The periodic times and the mean radii of the orbits are ${T_1},\,{T_2}$ and ${r_1},\,{r_2}$ respectively. The ratio ${T_1}/{T_2}$ is equal to
The value of $g$ at the surface of earth is $9.8 \,m / s ^2$. Then the value of ' $g$ ' at a place $480 \,km$ above the surface of the earth will be nearly .......... $m / s ^2$ (radius of the earth is $6400 \,km$ )
A particle of mass $M$ is placed at the centre of a uniform spherical shell of mass $2M$ and radius $R$. The gravitational potential on the surface of the shell is
Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to
The dependence of acceleration due to gravity $g$ on the distance $r$ from the centre of the earth assumed to be a sphere of radius $R$ of uniform density is as shown figure below
The correct figure is