Suppose the earth increases its speed of rotation . At what new time period will the weightof a body on the equator becomes zero? Take $g=10\frac{m}{s^2}$ and radius of the earth $R=6400km$.

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass $=5.98\times {10}^{24}kg$) have to be compresed to be a black hole?

A satellite of mass $m$ is orbiting the earth (of radius $R$) at a height $h$ from its surface. The total energy of the satellite in terms of $g_0$, the value of acceleration due to gravity at the earth's surface,

Two stars each of one solar mass $(=2\times 10^{30}kg)$ are approaching each other for a head on collision. When they are a distance $10^{9}km$, their speeds are negligible. What is the speed with which they collide ? The radius of each star is $10^{4}km$. Assume the stars to remain undistorted until they collide. (Use the known value of G).

The earth is assumed to be a sphere of raduis $R$. A plateform is arranged at a height $R$ from the surface of the $f{v}_e$, where $v_e$ is its escape velocity form the surface of the earth. The value of $f$ is

 Buoyant force on an object immersed in a liquid acts in upward direction.

Why does a black of wood held under water rise to the surface when released?