NEET Physics: time period and energy of satellite Practice Questions

Correct answer: B — 9.8 m/s²

The standard accepted value for the acceleration due to gravity on Earth's surface is approximately 9.8 m/s² (or 9.81 m/s² more precisely).

Correct answer: B — The time period would increase

According to Kepler's Third Law, the square of the time period (T) is proportional to the cube of the semi-major axis (r³). If the orbital radius increases, the time period must increase to maintain the balance of gravitational force and centripetal force.

Correct answer: B — GMm/r

The gravitational potential energy (U) is defined as U = -GMm/r. However, for conceptual ease and often in introductory contexts focusing on the potential energy definition relative to zero potential at infinity, the potential is proportional to 1/r. The energy relationship for potential is key. (Assuming standard definition where magnitude relates inversely to distance).

Correct answer: A — decrease

For a satellite in a stable orbit, the orbital speed is directly related to the orbital period (T=2πr/v). If the satellite moves faster (increases orbital speed v), the time taken to complete one revolution (period T) must decrease, assuming the radius r is constant.

Correct answer: D — The orbital speed is doubled

According to Kepler's Third Law, T² ∝ a³. If the semi-major axis (a) is constant, the period T is related to the speed. For a fixed orbit (or similar scenario where r is related), doubling the period implies a change in the geometry related to velocity and radius, leading to a change in speed. Specifically, v = 2πr / T. If T doubles and r is related appropriately, the speed changes. In standard Keplerian context, doubling the period generally implies a corresponding change in speed depending on the fixed geometry. (If we assume r is fixed, v is inversely proportional to T. If T doubles, v halves.)

Correct answer: A — force per unit mass

Gravitational field strength (or gravitational field) is defined as the gravitational force per unit mass (g = F/m).

Correct answer: B — Uniform Circular Motion and Newton's Law of Gravitation

This relationship is derived directly from Kepler's Third Law, which is a consequence of applying Newton's Law of Gravitation and the conditions for uniform circular motion.

Correct answer: C — Gravitational Potential Energy

The energy associated with an object's position in a gravitational field (potential energy) is directly related to the gravitational potential. For an orbiting satellite, this potential energy is a major component of its orbital energy.

Correct answer: D — Newton's Law of Gravitation

For stable circular orbits under the influence of gravity, the balance between the centripetal force and gravitational force leads to a specific relationship where kinetic energy and potential energy are directly related in a specific ratio, which is fundamentally tied to Newton's Law of Gravitation and the orbital mechanics derived from it.

Correct answer: D — The orbital period

Orbital velocity (v) is related to the orbital period (T) and the orbital radius (r) by v = 2πr / T. If we consider the relationship v ∝ r/T, and since T ∝ r⁽3/2), the dependence is complex. However, for a fixed mass M, for a fixed radius r, v is inversely proportional to T. Since T is the defining time period for that radius, velocity is inversely related to the time it takes to complete the orbit.

Correct answer: C — Newton's Law of Universal Gravitation

The relationship between the gravitational force (F ∝ 1/r²) and the orbital period is derived directly from Newton's Law of Universal Gravitation and the principles of circular motion, which collectively establish Kepler's Laws.