NEET Gravitation — Set 22

Question 1

Why did Newton conclude that the gravitational force decreases with the square of the distance?

Accepted Answer

Newton observed that the centripetal acceleration of the Moon ($ a_m = \frac{V^2}{R_m} $) was much smaller than the acceleration due to gravity on Earth’s surface ($ g $), and their ratio matched the inverse square of their distances from Earth’s center ($ \frac{g}{a_m} \approx \frac{R_m^2}{R_E^2} $).

Question 2

Why is the escape speed independent of the mass of the object being launched?

Accepted Answer

Escape speed as $ v_e = \sqrt{\frac{2 G M}{R}} $. The mass $ m $ of the object cancels out in the energy conservation equation ($ \frac{1}{2} m v_e^2 = \frac{G M m}{R} $), making $ v_e $ dependent only on the planet’s mass $ M $ and radius $ R $.

Question 3

Which of the following statements is incorrect about $ g $ variation?

Accepted Answer

$ g $ decreases with altitude (option 1 correct), depth (option 2 correct), and is zero at the center (option 4 correct). Option 3 is incorrect as $ g $ decreases, not increases, below the surface.

NEET Physics: Gravitation — Practice Set 22

Q1. Why did Newton conclude that the gravitational force decreases with the square of the distance?

Q2. Why is the escape speed independent of the mass of the object being launched?

Q3. Which of the following statements is incorrect about \( g \) variation?

Q4. What is the minimum speed to escape from \( 3 R_E \) from Earth’s center? (\( g = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} \))

Q5. A moon orbits a planet with a period of 7 days and radius \( 5 \times 10^8 \, \text{m} \). What is the planet’s mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2, 1 \, \text{day} = 86400 \, \text{s} \))

Q6. A planet has a moon with an orbital radius of \( 5 \times 10^8 \, \text{m} \) and a period of 10 days. 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 Earth at a height equal to \( R_E/2 \). What is its orbital speed? (\( g = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} \))

Q8. How much energy is required to move a \( 700 \, \text{kg} \) satellite from \( 11 R_E \) to \( 22 R_E \) from Earth’s center? (\( M_E = 6 \times 10^{24} \, \text{kg}, R_E = 6.4 \times 10^6 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q9. What is the minimum speed to escape from \( 10 R_E \) from Earth’s center? (\( g = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} \))

Q10. Why does an object require more energy to escape from a higher altitude than to reach that altitude?