NEET Gravitation — Set 13

Question 1

Why does Kepler’s first law indicate that planetary orbits are not perfectly circular?

Accepted Answer

Kepler’s first law (law of orbits) describes planetary orbits as ellipses with the Sun at one focus, not circles (a special case of an ellipse). This deviation from circular motion reflects the real dynamics of gravitational interaction.

Question 2

Why is the gravitational potential energy negative in a bound system?

Accepted Answer

Gravitational potential energy as $ V = -\frac{G M m}{r} $, with zero at infinity. For a bound system (e.g., orbit), the negative value indicates that work must be done to separate the objects to infinity, reflecting gravitational attraction.

Question 3

What is the gravitational potential due to Earth at $ 3.84 \times 10^7 \, \text{m} $ from its center? ($ M_E = 6 \times 10^{24} \, \text{kg}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 $)

Accepted Answer

$ U = -\frac{G M_E}{r} $. $ U = -\frac{6.67 \times 10^{-11} \times 6 \times 10^{24}}{3.84 \times 10^7} $. $ U = -1.0417 \times 10^7 \, \text{J/kg} $.

NEET Physics: Gravitation — Practice Set 13

Q1. Why does Kepler’s first law indicate that planetary orbits are not perfectly circular?

Q2. Why is the gravitational potential energy negative in a bound system?

Q3. What is the gravitational potential due to Earth at \( 3.84 \times 10^7 \, \text{m} \) from its center? (\( M_E = 6 \times 10^{24} \, \text{kg}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q4. Why does a satellite in a circular orbit have negative total energy?

Q5. What is the escape speed from a planet with \( g = 4.9 \, \text{m/s}^2 \) and radius \( 3.2 \times 10^6 \, \text{m} \)?

Q6. A moon orbits a planet with a period of 13 days and radius \( 1.0 \times 10^9 \, \text{m} \). 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. Three \( 2 \, \text{kg} \) masses form an equilateral triangle of side \( 1 \, \text{m} \). What is the potential energy? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q8. How much energy is required to move a \( 600 \, \text{kg} \) satellite from \( 10 R_E \) to \( 20 R_E \) 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 ensures that a satellite remains in a stable circular orbit?

Q10. A body is projected from Earth with \( 13 \, \text{km/s} \). What is its speed far away? (Escape speed = \( 11.2 \, \text{km/s} \))