NEET Gravitation — Set 1

Question 1

Which of the following statements is correct about the gravitational force between two masses?

Accepted Answer

$ F = G \frac{m_1 m_2}{r^2} $ is always attractive, as masses are positive and the force vector points toward each other, making option 1 correct.

Question 2

Two masses $ 8 \, \text{kg} $ and $ 16 \, \text{kg} $ are $ 16 \, \text{m} $ apart. What is the gravitational potential at a point $ 7 \, \text{m} $ from the $ 8 \, \text{kg} $ mass? ($ G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 $)

Accepted Answer

Distance to $ 16 \, \text{kg} $: $ 16 - 7 = 9 \, \text{m} $. $ U = -\frac{G m_1}{r_1} - \frac{G m_2}{r_2} $. $ U = -6.67 \times 10^{-11} \left(\frac{8}{7} + \frac{16}{9}\right) $. $ U = -6.67 \times 10^{-11} (1.143 + 1.778) \approx -1.95 \times 10^{-10} \, \text{J/kg} $.

Question 3

What is the kinetic energy of a $ 700 \, \text{kg} $ satellite at $ 9 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 = 9 R_E = 5.76 \times 10^7 \, \text{m} $. $ K = \frac{6.67 \times 10^{-11} \times 6 \times 10^{24} \times 700}{2 \times 5.76 \times 10^7} $. $ K = \frac{2.801 \times 10^{17}}{1.152 \times 10^8} \approx 2.43 \times 10^9 \, \text{J} $.

NEET Physics: Gravitation — Practice Set 1

Q1. Which of the following statements is correct about the gravitational force between two masses?

Q2. Two masses \( 8 \, \text{kg} \) and \( 16 \, \text{kg} \) are \( 16 \, \text{m} \) apart. What is the gravitational potential at a point \( 7 \, \text{m} \) from the \( 8 \, \text{kg} \) mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q3. What is the kinetic energy of a \( 700 \, \text{kg} \) satellite at \( 9 R_E \) from Earth’s center? (\( M_E = 6 \times 10^{24} \, \text{kg}, R_E = 6.4 \times 10^6 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q4. Two masses \( 6 \, \text{kg} \) and \( 12 \, \text{kg} \) are \( 12 \, \text{m} \) apart. What is the gravitational potential at a point \( 5 \, \text{m} \) from the \( 6 \, \text{kg} \) mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q5. A satellite’s period near Earth’s surface is 88 minutes. What is its period at \( h = 4 R_E \)? (\( R_E = 6.4 \times 10^6 \, \text{m} \))

Q6. Which property of gravitational force allows us to define a potential energy?

Q7. What does the inverse-square nature of gravitational force imply about its range?

Q8. What is the escape speed from a planet with mass \( 2.7 \times 10^{24} \, \text{kg} \) and radius \( 4.5 \times 10^6 \, \text{m} \)? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q9. A satellite orbits a planet at \( 7 \times 10^7 \, \text{m} \) from its center with a period of 18 hours. What is the planet’s mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q10. A body is launched from Earth at \( 14.5 \, \text{km/s} \). What is its speed at infinity? (Escape speed = \( 11.2 \, \text{km/s} \))

Q11. Four masses of \( 2 \, \text{kg} \) each are at the vertices of a square with side \( 4 \, \text{m} \). What is the net force on one mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q12. A projectile is launched at \( 6 \, \text{km/s} \) from Earth’s surface. What is its maximum distance from the center? (Escape speed = \( 11.2 \, \text{km/s}, R_E = 6.4 \times 10^6 \, \text{m} \))

Q13. A body experiences \( g = 7.35 \, \text{m/s}^2 \) at a certain height above Earth. What is the height? (\( g_0 = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} \))

Q14. A planet orbits the Sun with a period of 3 years. If Earth’s orbital radius is \( 1.5 \times 10^{11} \, \text{m} \), what is its semi-major axis?

Q15. Which of the following statements is incorrect about gravitational force?