#concept question

Potential Energy of Mass Systems

What does the constant k in Kepler’s third law (T2\=kr3) depend on for satellites?

T2 = 4π2GMEr3 for satellites, where k = 4π2GME. Thus, k depends on the mass of the central body (Earth) and universal constants, not the satellite’s mass. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Mass of the central body. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.

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Variation of g with Height and Depth

What does the zero gravitational potential at infinity imply about gravitational systems?

V = 0 at r→∞ as a convention, implying that all bound systems (e.g., orbits) have negative potential energy, requiring external work to unbind them to infinity. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Bound systems have negative energy. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.

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Variation of g with Height and Depth

Why is the gravitational force considered a conservative force?

The work done by gravity is independent of the path taken and depends only on the initial and final positions. This path independence defines a conservative force, allowing a potential energy function to be defined.

Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.

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Universal Law of Gravitation

Why does the acceleration due to gravity decrease both above and below Earth’s surface?

Above the surface, g decreases as g(h)∝1/(RE+h)2. Below the surface, only the mass inside a radius r

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Universal Law of Gravitation

Which of the following statements is incorrect about a satellite in orbit?

otal energy is negative (option 1 correct), kinetic energy varies in elliptical orbits (option 2 correct), and gravity provides centripetal force (option 3 correct). Option 4 is incorrect as speed decreases with altitude.

Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.

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