NEET Gravitation — Set 14

Question 1

What is the minimum speed to escape from $ 8 R_E $ from Earth’s center? ($ g = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} $)

Accepted Answer

$ v_e = \sqrt{\frac{2 g R_E^2}{8 R_E}} = \sqrt{\frac{2 \times 9.8 \times 6.4 \times 10^6}{8}} $. $ v_e = \sqrt{1.568 \times 10^7} \approx 3.96 \times 10^3 \, \text{m/s} \approx 4.0 \, \text{km/s} $.

Question 2

What is the kinetic energy of a $ 300 \, \text{kg} $ satellite at $ 5 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 $)

Accepted Answer

$ K = \frac{G M_E m}{2 r} $. $ r = 5 R_E = 3.2 \times 10^7 \, \text{m} $. $ K = \frac{6.67 \times 10^{-11} \times 6 \times 10^{24} \times 300}{2 \times 3.2 \times 10^7} $. $ K = \frac{1.201 \times 10^{17}}{6.4 \times 10^7} \approx 1.88 \times 10^9 \, \text{J} $.

Question 3

What is the escape speed from a planet with mass $ 4.5 \times 10^{24} \, \text{kg} $ and radius $ 6 \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 4.5 \times 10^{24}}{6 \times 10^6}} $. $ v_e = \sqrt{1.0005 \times 10^8} \approx 1.00 \times 10^4 \, \text{m/s} = 10.0 \, \text{km/s} $.

NEET Physics: Gravitation — Practice Set 14

Q1. What is the minimum speed to escape from \( 8 R_E \) from Earth’s center? (\( g = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} \))

Q2. What is the kinetic energy of a \( 300 \, \text{kg} \) satellite at \( 5 R_E \) from Earth’s center? (\( M_E = 6 \times 10^{24} \, \text{kg}, R_E = 6.4 \times 10^6 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q3. What is the escape speed from a planet with mass \( 4.5 \times 10^{24} \, \text{kg} \) and radius \( 6 \times 10^6 \, \text{m} \)? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q4. A satellite near Earth has a period of 82 minutes. What is its period at \( h = 9 R_E \)? (\( R_E = 6.4 \times 10^6 \, \text{m} \))

Q5. Why is the value of \( g \) maximum at Earth’s surface?

Q6. Four \( 8 \, \text{kg} \) masses form a square of side \( 8 \, \text{m} \). What is the potential energy of the system? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q7. What is the minimum speed to escape from \( 7 R_E \) from Earth’s center? (\( g = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} \))

Q8. A \( 5 \, \text{kg} \) mass is moved from \( 5 R_E \) to \( 10 R_E \) from Earth’s center. What is the change in potential energy? (\( M_E = 6 \times 10^{24} \, \text{kg}, R_E = 6.4 \times 10^6 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q9. What is the gravitational potential energy of a \( 2 \, \text{kg} \) mass at a height of \( 6.4 \times 10^6 \, \text{m} \) above Earth’s surface? (\( M_E = 6 \times 10^{24} \, \text{kg}, R_E = 6.4 \times 10^6 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q10. Two masses \( 3 \, \text{kg} \) and \( 6 \, \text{kg} \) are \( 6 \, \text{m} \) apart. What is the gravitational potential at a point \( 2 \, \text{m} \) from the \( 3 \, \text{kg} \) mass on the line joining them? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))