The escape velocity of an object from the gravitational field of a planet I. Increases with the mass of the…

Analyzing the question: We need to decide which statements about escape velocity are true.

Concept: Escape velocity is the minimum speed needed for an object to escape a planet's gravitational pull without further propulsion.

Formula:

v = √(2GM/R)

where G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet.

(It also equals √(2gR).)

Checking each statement:

• I. Increases with the mass of the object. False. The mass of the object (m) cancels out when we equate kinetic energy to gravitational potential energy: ½mv² = GMm/R → v² = 2GM/R So escape velocity does not depend on the object's mass.

• II. Increases with the mass of the planet. True. v is proportional to √M, so a larger planetary mass gives a larger escape velocity (for a fixed radius).

• III. Is smaller on the moon than on the earth. True. The Moon has a much smaller mass and radius. Its escape velocity is about 2.4 km/s, compared to about 11.2 km/s on Earth.

So statements II and III are correct.

Answer: D (II and III only)

Exam tip: Remember that escape velocity depends on the planet (M and R) only, never on the mass of the escaping object. Any option claiming the object's mass matters can be eliminated immediately.