NEET Gravitation — Set 19

Question 1

A satellite orbits Earth at $ 19 R_E $ from the center. What is its orbital speed? ($ g = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} $)

Accepted Answer

$ v = \sqrt{\frac{g R_E^2}{r}} $. $ r = 19 R_E $, $ v = \sqrt{\frac{9.8 \times 6.4 \times 10^6}{19}} $. $ v = \sqrt{3.301 \times 10^6} \approx 1.82 \times 10^3 \, \text{m/s} $.

Question 2

A projectile is launched at $ 1 \, \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} $)

Accepted Answer

$ \frac{1}{2} v_i^2 - \frac{v_e^2}{2} = -\frac{v_e^2}{2} \frac{R_E}{r} $. $ 0.5 - 62.72 = -62.72 \frac{R_E}{r} $. $ \frac{r}{R_E} = \frac{62.72}{62.22} \approx 1.008 $. $ r = 1.008 \times 6.4 \times 10^6 \approx 6.45 \times 10^6 \, \text{m} $.

Question 3

Which of the following statements is correct about the gravitational force inside a hollow spherical shell?

Accepted Answer

The net gravitational force inside a uniform hollow spherical shell is zero due to symmetry, making option 2 correct.

NEET Physics: Gravitation — Practice Set 19

Q1. A satellite orbits Earth at \( 19 R_E \) from the center. What is its orbital speed? (\( g = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} \))

Q2. A projectile is launched at \( 1 \, \text{km/s} \) from Earth’s surface. What is its maximum distance from the center? (Escape speed = \( 11.2 \, \text{km/s}, R_E = 6.4 \times 10^6 \, \text{m} \))

Q3. Which of the following statements is correct about the gravitational force inside a hollow spherical shell?

Q4. A projectile is launched at \( 9 \, \text{km/s} \) from Earth’s surface. What is its maximum distance from the center? (Escape speed = \( 11.2 \, \text{km/s}, R_E = 6.4 \times 10^6 \, \text{m} \))

Q5. Why does the total energy of a satellite in an elliptical orbit remain constant?

Q6. A \( 250 \, \text{kg} \) satellite orbits Earth at \( 6 R_E \) from the center. What is its total energy? (\( M_E = 6 \times 10^{24} \, \text{kg}, R_E = 6.4 \times 10^6 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q7. What is the significance of the negative sign in the gravitational potential energy formula \( V = -\frac{G M m}{r} \)?

Q8. At what height above Earth’s surface is \( g \) reduced to \( 7.84 \, \text{m/s}^2 \)? (\( g_0 = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} \))

Q9. A satellite orbits Earth at \( 11 R_E \) from the center. What is its orbital speed? (\( g = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} \))

Q10. Four \( 7 \, \text{kg} \) masses form a square of side \( 7 \, \text{m} \). What is the potential energy of the system? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))