The condition for a uniform spherical mass m of radius r to be a black hole is [ $G$ = gravitational constant and $g$ = acceleration due to gravity]
${(2Gm/r)^{1/2}} \le c$
${(2Gm/r)^{1/2}} = c$
${(2Gm/r)^{1/2}} \ge c$
${(gm/r)^{1/2}} \ge c$
Two identical spheres are placed in contact with each other. The force of gravitation between the spheres will be proportional to ($R =$ radius of each sphere)
What should be the angular speed of the earth, so that a body lying on the equator may appear weightlessness $(g = 10\,m/s^2, R = 6400\,km)$
Figure shows the variation of the gravitatioal acceleration $a_g$ of four planets with the radial distance $r$ from the centre of the planet for $r\geq $ radius of the planet. Plots $1$ and $2$ coincide for $r\geq R_2$ and plots $3$ and $4$ coincide for $r \geq R_4$. The sequence of the planets in the descending order of their densities is
Suppose the earth stopped rotating. Then, the weight a body will
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