NEET Gravitation — Set 21

Question 1

What is the escape speed from a planet of mass $ 4.8 \times 10^{24} \, \text{kg} $ and radius $ 5 \times 10^6 \, \text{m} $? ($ G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 $)

Accepted Answer

$ v_e = \sqrt{\frac{2 G M}{R}} $. $ v_e = \sqrt{\frac{2 \times 6.67 \times 10^{-11} \times 4.8 \times 10^{24}}{5 \times 10^6}} $. $ v_e = \sqrt{6.403 \times 10^7} \approx 8.0 \times 10^3 \, \text{m/s} = 8.0 \, \text{km/s} $.

Question 2

What is the gravitational force on a $ 13 \, \text{kg} $ mass $ 11 \, \text{m} $ from the center of a spherical shell of mass $ 700 \, \text{kg} $ and radius $ 9 \, \text{m} $? ($ G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 $)

Accepted Answer

Outside shell: $ F = \frac{G M m}{r^2} $. $ F = \frac{6.67 \times 10^{-11} \times 700 \times 13}{11^2} $. $ F = \frac{6.0689 \times 10^{-8}}{121} \approx 5.02 \times 10^{-10} \, \text{N} $.

Question 3

What property of the gravitational force allows Newton’s law to apply to extended objects?

Accepted Answer

The gravitational force obeys the principle of superposition, meaning the total force on a body is the vector sum of forces from individual point masses. This allows the law to extend to composite objects by summing contributions.

NEET Physics: Gravitation — Practice Set 21

Q1. What is the escape speed from a planet of mass \( 4.8 \times 10^{24} \, \text{kg} \) and radius \( 5 \times 10^6 \, \text{m} \)? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q2. What is the gravitational force on a \( 13 \, \text{kg} \) mass \( 11 \, \text{m} \) from the center of a spherical shell of mass \( 700 \, \text{kg} \) and radius \( 9 \, \text{m} \)? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q3. What property of the gravitational force allows Newton’s law to apply to extended objects?

Q4. What causes the elliptical shape of planetary orbits according to Newton’s theory?

Q5. Which of the following statements is incorrect about gravitational potential energy?

Q6. What causes the variation in kinetic energy of a satellite in an elliptical orbit?

Q7. Four \( 9 \, \text{kg} \) masses form a square of side \( 9 \, \text{m} \). What is the potential energy of the system? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q8. What is the gravitational potential due to Earth at \( 1.28 \times 10^7 \, \text{m} \) from its center? (\( M_E = 6 \times 10^{24} \, \text{kg}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q9. What is the primary reason the gravitational force inside a uniform spherical shell is zero?

Q10. Two masses \( 4 \, \text{kg} \) and \( 8 \, \text{kg} \) are \( 8 \, \text{m} \) apart. What is the gravitational potential at a point \( 3 \, \text{m} \) from the \( 4 \, \text{kg} \) mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))