If all objects on the equator of earth feel weightless then the duration of the day will nearly become ....... $hr$

The angular speed of earth, so that the object on equator may appear weightless, is $(g = 10\,m/{s^2}$, radius of earth $6400\, km$)

A body weights $49\,N$ on a spring balance at the north pole. ..... $N$ will be its weight recorded on the same weighing machine, if it is shifted to the equator?

(Use $g=\frac{G M}{R^{2}}=9.8 \,ms ^{-2}$ and radius of earth, $R =6400\, km .]$

A body weighs $72\; N$ on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth ?

A uniform spherical planet (Radius $R$) has acceleration due to gravity at its surface $g.$ Points $P$ and $Q$ located inside and outside the planet have acceleration due to gravity $\frac{g}{4} .$ Maximum possible separation between $P$ and $Q$ is

A man of $50\, kg$ mass is standing in a gravity free space at a height of $10\, m$ above the floor. He throws a stone of $0.5\, kg$ mass downwards with a speed $2\, m/s$. When the stone reaches the floor, the distance of the man above the floor will be ...... $m$