A ball is launched from the top of Mt. Everest which is at elevation of $9000 \,m$. The ball moves in circular orbit around earth. Acceleration due to gravity near the earth's surface is $g$. The magnitude of the ball's acceleration while in orbit is

The radius of the earth is $6400\, km$ and $g = 10\,m/{\sec ^2}$. In order that a body of $5 \,kg$ weighs zero at the equator, the angular speed of the earth is

A projectile is fired from the surface of the earth with a velocity of $5\, ms^{-1}$ and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3\, ms^{-1}$ at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in $ms^{-2}$) is (given $g = 9.8\, m/s^2$)

A pendulum clock is set to give correct time at the sea level. This clock is moved to hill station at an altitude of $2500\, m$ above the sea level. In order to keep correct time of the hill station, the length of the pendulum

If density of a planet is double that of the earth and the radius $1.5$ times that of the earth, the acceleration due to gravity on the surface of the planet is ……..