NEET Gravitation — Set 24

Question 1

A body is launched from Earth at $ 12 \, \text{km/s} $. What is its speed at infinity? (Escape speed = $ 11.2 \, \text{km/s} $)

Accepted Answer

$ v_f^2 = v_i^2 - v_e^2 $. $ v_f^2 = (12)^2 - (11.2)^2 = 144 - 125.44 = 18.56 $. $ v_f = \sqrt{18.56} \approx 4.31 \, \text{km/s} $.

Question 2

What is the kinetic energy of a $ 900 \, \text{kg} $ satellite at $ 11 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 = 11 R_E = 7.04 \times 10^7 \, \text{m} $. $ K = \frac{6.67 \times 10^{-11} \times 6 \times 10^{24} \times 900}{2 \times 7.04 \times 10^7} $. $ K = \frac{3.602 \times 10^{17}}{1.408 \times 10^8} \approx 2.56 \times 10^9 \, \text{J} $.

Question 3

What is the escape speed from a planet with mass $ 9 \times 10^{23} \, \text{kg} $ and radius $ 2.5 \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 9 \times 10^{23}}{2.5 \times 10^6}} $. $ v_e = \sqrt{4.801 \times 10^7} \approx 6.93 \times 10^3 \, \text{m/s} \approx 6.9 \, \text{km/s} $.

NEET Physics: Gravitation — Practice Set 24

Q1. A body is launched from Earth at \( 12 \, \text{km/s} \). What is its speed at infinity? (Escape speed = \( 11.2 \, \text{km/s} \))

Q2. What is the kinetic energy of a \( 900 \, \text{kg} \) satellite at \( 11 R_E \) 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 \( 9 \times 10^{23} \, \text{kg} \) and radius \( 2.5 \times 10^6 \, \text{m} \)? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q4. A body is launched from Earth at \( 15.5 \, \text{km/s} \). What is its speed at infinity? (Escape speed = \( 11.2 \, \text{km/s} \))

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

Q6. A moon orbits a planet with a period of 10 days and radius \( 7 \times 10^8 \, \text{m} \). What is the planet’s mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2, 1 \, \text{day} = 86400 \, \text{s} \))

Q7. A satellite orbits a planet at \( 3 \times 10^7 \, \text{m} \) from its center with a period of 6 hours. What is the planet’s mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q8. A satellite near Earth has a period of 89 minutes. What is its period at \( h = 7 R_E \)? (\( R_E = 6.4 \times 10^6 \, \text{m} \))

Q9. Why is the gravitational force zero at the center of a uniform solid sphere?

Q10. Why does the work done by gravity in moving an object depend only on the vertical displacement near Earth’s surface?