The escape velocity from a planet is $V_e.$  A tunnel is dug along the diameter of the planet and a small body dropped into it. The speed of the body at the centre of the planet will be

According to Kepler’s law the time period of a satellite varies with its radius as

A geostationary satellite is orbiting the earth at a height of $6\, R$ from the earth’s surface ($R$ is the earth’s radius ). What is the period of rotation of another satellite at a height of $2.5\, R$ from the earth’s surface

A geostationary satellite is orbiting the earth at a height of $6\,R$ above the surface of  earth ($R$ is the radius of earth). The time period of another satellite at a height of $2.5\,R$ from the surface of the earth is :-

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

Which of the following graph represents the variations of acceleration due to gravity $(g)$ with distance $r$ from the centre of earth?