Gravitation

Two point masses of 2 kg and 8 kg are placed 4 m apart. What is the gravitational force between them? (G = 6.67 × 10⁻¹¹ N·m²/kg²)

If the distance between two point masses is doubled, the gravitational force between them becomes:

The gravitational field intensity at a distance r from a point mass is 9 × 10⁻⁹ N/kg. What is the field intensity at a distance 3r from the same mass?

A solid sphere of mass M and radius R has a point at distance R/2 from its centre. What is the field intensity there, as a fraction of the field intensity at the surface?

At what height above Earth's surface does the acceleration due to gravity reduce to one-fourth of its surface value? (R = radius of Earth)

At what depth below Earth's surface does the value of g reduce to 75% of its surface value?

If Earth suddenly stopped rotating about its own axis, the value of g would:

Find the gravitational potential energy of a 5 kg mass at Earth's surface, given GM/R = 6.4 × 10⁷ J/kg.

The gravitational potential at a certain point is −16 J/kg. What is the potential energy of a 3 kg mass placed at that point?

A 2 kg mass is raised from Earth's surface to a height equal to Earth's radius R. Taking g = 10 m/s² and R = 6400 km, find the work done against gravity.

If Earth's radius were halved while its mass stayed the same, the escape velocity from its surface would:

A planet has the same mass as Earth but twice Earth's radius. In terms of Earth's escape velocity v_e, the escape velocity from this planet's surface is:

A planet orbits the Sun at twice Earth's orbital radius. Using Kepler's third law, find its time period in years.

A planet's distance from the Sun at perihelion is half its distance at aphelion. What is the ratio of its speed at perihelion to its speed at aphelion?

Two satellites orbit Earth at radii R and 4R. What is the ratio of their orbital velocities v₁ : v₂?

A satellite orbits at a height equal to Earth's radius R above the surface, so its orbital radius is 2R. If T₀ is the time period for a satellite very close to Earth's surface, find this satellite's time period.

A satellite of mass m orbits Earth with kinetic energy K. What is its total mechanical energy?

A 500 kg satellite orbits Earth at a radius of 8000 km. Given GM = 4 × 10¹⁴ m³/s² for Earth, find the binding energy of the satellite.