Gravitation Quiz-1

If ‘g’ is the acceleration due to gravity on the surface of the earth, the percentage gain in potential energy of an object, when it is raised from sea level to an altitude equal to a fourth of earth’s radius is:

An astronaut in artificial satellite experiences weightlessness because:

The acceleration due to gravity of earth, on its surface, is $9.81\, ms^{-2}$

If somehow on its own the radius of earth were to decrease by $\frac1n$ of its present value, keeping its mass the same, the percentage increase in its duration of the day will be:

A pendulum is shifted from the surface of the earth (R = 6400 Km) to a position of 400 m above the surface. The time loss for the pendulum in a day is:

The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to 25% of that on the surface of the earth. If the radius of the earth is R, the radius of the planet is:

A satellite of mass ‘m’ is orbiting close to the surface of earth (R = 6400 Km). The satellite has a kinetic energy of K. An additional kinetic energy of equal amount is given to this satellite. The radius of its orbit will now become equal to:

At what depth, from the surface of the earth would the value of acceleration due to gravity become equal to its value at a height of 9800 km from the surface of the earth? (Given: radius of earth = 6400 km)

Imagine that a body is projected from the surface of the earth with a speed equal to 40% of the escape speed from earth. What is the maximum height attained by the body? (R = 6400 km is the radius of the earth).

Imagine that the universal gravitational constant (G) becomes time-dependent. For a particle, moving under such a gravitational field, which of the following quantities would be still conserved?