Gravitation — Flashcards & Quiz

Q1: State Newton's Law of Universal Gravitation.

F = GMm/r², where F is the gravitational force, G = 6.674 × 10⁻¹¹ N·m²/kg² is the gravitational constant, M and m are the two masses, and r is the distance between their centres. The force is always attractive and acts along the line joining the centres.

Q2: What is gravitational field strength and how is it related to g?

Gravitational field strength g = F/m = GM/r² (N/kg or m/s²). It equals the acceleration due to gravity at that point. At Earth's surface: g ≈ 9.8 m/s². It decreases with altitude as r increases. Inside Earth, g decreases linearly to zero at the centre.

Q3: What is gravitational potential energy in the universal context?

U = -GMm/r (negative because work must be done AGAINST gravity to separate masses). At infinity, U = 0. As r decreases (closer to the central mass), U becomes more negative. The change in GPE: ΔU = GMm(1/r₁ - 1/r₂).

Q4: What is the gravitational field and how is it represented?

A gravitational field is the region around a mass where another mass experiences a gravitational force. Represented by field lines pointing toward the mass (direction a test mass would accelerate). Closer field lines = stronger field. For a uniform field (near Earth's surface), lines are parallel and equally spaced.

Q5: What is the total mechanical energy of an orbiting satellite?

E_total = KE + U = ½mv² + (-GMm/r). For a circular orbit: v² = GM/r, so KE = GMm/(2r). Therefore E_total = GMm/(2r) - GMm/r = -GMm/(2r). Total energy is negative (bound orbit) and equals half the potential energy.

Q1: Gravitational force between two objects doubles when the distance between them is halved.

Answer: FALSE

F = GMm/r². If r is halved: F = GMm/(r/2)² = GMm/(r²/4) = 4GMm/r². The force QUADRUPLES (inverse square law). Doubling occurs when one mass doubles.

Q2: Gravitational field strength at a point depends on the mass of the test object placed there.

Answer: FALSE

Field strength g = GM/r² depends only on the SOURCE mass M and distance r. The test mass cancels out when deriving g = F/m. Field strength is a property of the field itself, not the test mass.

Q3: Gravitational potential energy is always negative for objects in bound orbits.

Answer: TRUE

U = -GMm/r is always negative (as r > 0). For bound orbits, total energy E = -GMm/(2r) is also negative. An object escapes when E ≥ 0.