Unit 5 Summative Assessment: Gravitational Field

What are the SI base units of the Universal Gravitational Constant G?

If the distance between two point masses is reduced to one-third of its original value, by what factor does the gravitational force between them change?

Two identical lead spheres, each of mass 50.0 kg, have their centers separated by 0.50 m. Calculate the magnitude of the gravitational attraction between them in nN (nanoNewtons). Take G = 6.674 × 10⁻¹¹ N m² kg⁻².

How is the gravitational field strength (g) at a point in a gravitational field defined?

The radius of planet Mars is 3.39 × 10⁶ m and its mass is 6.42 × 10²³ kg. Calculate the gravitational acceleration at the surface of Mars in m s⁻². Take G = 6.674 × 10⁻¹¹ N m² kg⁻².

At what altitude h above the Earth’s surface (radius R) is the gravitational field strength equal to g₀/4, where g₀ is the field strength at the surface?

Assuming the Earth is a uniform solid sphere of radius R, how does the gravitational field strength g vary at depth d below the surface?

Why is the measured value of gravitational acceleration g slightly greater at the poles than at the equator of the Earth?

The mass of the Earth is 81 times the mass of the Moon, and the distance between their centers is 3.84 × 10⁸ m. Find the distance from the center of the Earth to the neutral point between them (where the net gravitational field is zero) in units of 10⁸ m.

Two point masses M and 4M are separated by a distance d. Where should a third mass m be placed along the line connecting them so that the net gravitational force on m is zero?

Why is gravitational potential at any finite distance from an isolated mass defined to be negative (taking V = 0 at infinity)?

Calculate the gravitational potential at the surface of the Earth in units of 10⁷ J kg⁻¹ (as a positive magnitude). Take Earth mass M = 5.972 × 10²⁴ kg, radius R = 6.371 × 10⁶ m, and G = 6.674 × 10⁻¹¹ N m² kg⁻².

What is the relationship between gravitational field intensity g and gravitational potential V at a distance r from a point mass?

Which of the following statements about equipotential surfaces in a gravitational field is FALSE?

A mass m is lifted from the surface of Earth (mass M, radius R) to an altitude h = R above the surface. What is the increase in its gravitational potential energy?

A 500 kg satellite is moved from an initial orbital radius of 7.0 × 10⁶ m to a higher orbit of radius 1.4 × 10⁷ m around the Earth (M = 5.972 × 10²⁴ kg). Calculate the change in gravitational potential energy in gigajoules (GJ). Take G = 6.674 × 10⁻¹¹ N m² kg⁻².

Two masses m and 2m are held at distance 2a apart. What is the gravitational potential at the midpoint between them?

How much work is required to bring a 10 kg mass from infinity to a point where the gravitational potential is -40 MJ kg⁻¹?

A body is released from rest at a height h above Earth’s surface. Neglecting air resistance, what is its speed v upon reaching the surface (Earth radius R, surface gravity g)?

A projectile is fired vertically upward from Earth’s surface with initial speed 4.0 km s⁻¹. To what maximum altitude in kilometers will it rise? Take Earth radius R = 6400 km and g = 9.80 m s⁻².