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]
${(2Gm/r)^{1/2}} \le c$
${(2Gm/r)^{1/2}} = c$
${(2Gm/r)^{1/2}} \ge c$
${(gm/r)^{1/2}} \ge c$
The kinetic energy needed to project a body of mass $m$ from the earth's surface (radius $R$ ) to infinity is
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 in figure below
A rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V.$ Assuming the radius of the earth to be $R$ and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is
The kinetic energy needed to project a body of mass $m$ from the earth's surface (radius $R$) to infinity is
A satellite can be in a geostationary orbit around a planet at a distance $r$ from the centre of the planet. If the angular velocity of the planet about its axis doubles, a satellite can now be in a geostationary orbit around the planet if its distance from the centre of the planet is