NEET Gravitation — Set 9

Question 1

What determines the escape speed from a planet?

Accepted Answer

Correct option: A

Question 2

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

Accepted Answer

In an elliptical orbit, speed varies (faster at perihelion, slower at aphelion) due to conservation of angular momentum, making option 3 correct.

Question 3

A $ 800 \, \text{kg} $ satellite orbits Earth at $ 12 R_E $ from the center. What is its total energy? ($ M_E = 6 \times 10^{24} \, \text{kg}, R_E = 6.4 \times 10^6 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 $)

Accepted Answer

$ E = -\frac{G M_E m}{2 r} $. $ r = 12 R_E = 7.68 \times 10^7 \, \text{m} $. $ E = -\frac{6.67 \times 10^{-11} \times 6 \times 10^{24} \times 800}{2 \times 7.68 \times 10^7} $. $ E = -\frac{3.202 \times 10^{17}}{1.536 \times 10^8} \approx -2.08 \times 10^9 \, \text{J} $.

NEET Physics: Gravitation — Practice Set 9

Q1. What determines the escape speed from a planet?

Q2. Which of the following statements is correct about a satellite in elliptical orbit?

Q3. A \( 800 \, \text{kg} \) satellite orbits Earth at \( 12 R_E \) from the center. What is its total energy? (\( M_E = 6 \times 10^{24} \, \text{kg}, R_E = 6.4 \times 10^6 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q4. Why is the gravitational force between two point masses always attractive?

Q5. Why does the gravitational force provide the necessary centripetal force for a circular orbit?

Q6. What is the gravitational force on a \( 2 \, \text{kg} \) mass inside a hollow spherical shell of mass \( 1000 \, \text{kg} \) and radius \( 1 \, \text{m} \)?

Q7. A body is launched from Earth at \( 11.8 \, \text{km/s} \). What is its speed at infinity? (Escape speed = \( 11.2 \, \text{km/s} \))

Q8. A body is launched from Earth at \( 13.5 \, \text{km/s} \). What is its speed at infinity? (Escape speed = \( 11.2 \, \text{km/s} \))

Q9. How much energy is required to move a \( 500 \, \text{kg} \) satellite from \( 9 R_E \) to \( 18 R_E \) from Earth’s center? (\( M_E = 6 \times 10^{24} \, \text{kg}, R_E = 6.4 \times 10^6 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q10. Why does an object need a minimum speed to escape Earth’s gravity?