NEET Gravitation — Set 10

Question 1

Why does the gravitational potential energy of two masses become more negative as they get closer?

Accepted Answer

$ V = -\frac{G M m}{r} $. As $ r $ decreases, the term $ -\frac{G M m}{r} $ becomes larger in magnitude (more negative), reflecting increased binding energy due to stronger attraction.

Question 2

Which of the following statements is incorrect about escape speed?

Accepted Answer

Escape speed ($ v_e = \sqrt{\frac{2 G M}{R}} $) is independent of the object’s mass (option 1 correct), depends on $ M $ and $ R $ (option 2 correct), and decreases with altitude (option 4 correct). Option 3 is incorrect as it does depend on the planet.

Question 3

A satellite orbits a planet at $ 4 \times 10^7 \, \text{m} $ from its center with a period of 8 hours. What is the planet’s mass? ($ G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 $)

Accepted Answer

$ M = \frac{4\pi^2 r^3}{G T^2} $. $ T = 8 \times 3600 = 28800 \, \text{s} $, $ T^2 = 8.2944 \times 10^8 \, \text{s}^2 $. $ r^3 = (4 \times 10^7)^3 = 6.4 \times 10^{22} \, \text{m}^3 $. $ M = \frac{4 \times (3.14)^2 \times 6.4 \times 10^{22}}{6.67 \times 10^{-11} \times 8.2944 \times 10^8} $. $ M = \frac{2.523 \times 10^{24}}{5.532 \times 10^{-2}} \approx 4.56 \times 10^{25} \, \text{kg} $.

NEET Physics: Gravitation — Practice Set 10

Q1. Why does the gravitational potential energy of two masses become more negative as they get closer?

Q2. Which of the following statements is incorrect about escape speed?

Q3. A satellite orbits a planet at \( 4 \times 10^7 \, \text{m} \) from its center with a period of 8 hours. What is the planet’s mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q4. What is the minimum speed required to escape from a point \( R_E \) above Earth’s surface? (\( R_E = 6.4 \times 10^6 \, \text{m}, g = 9.8 \, \text{m/s}^2 \))

Q5. Why can’t a satellite in a circular orbit have zero total energy?

Q6. Three masses of \( 15 \, \text{kg} \) each form an equilateral triangle with side \( 10 \, \text{m} \). What is the net force on one mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q7. What happens to the gravitational force on a point mass inside a hollow spherical shell?

Q8. Which of the following statements is incorrect about acceleration due to gravity?

Q9. What does Kepler’s third law reveal about the motion of planets farther from the Sun?

Q10. Why can’t the gravitational force on a point mass outside a spherical shell be zero?