Universal Law of Gravitation - UNSOLVED PRACTICE SET
Chapter: Gravitation | Topic: Universal Law of Gravitation
UNIVERSAL LAW OF GRAVITATION - UNSOLVED PRACTICE SET
Topic: Universal Law of Gravitation
Multiple Choice Questions
Q1. Newton's universal law of gravitation states that the gravitational force between two masses is:
- Directly proportional to the distance between them
- Inversely proportional to the square of the distance between them
- Independent of the distance between them
- Inversely proportional to the cube of the distance between them
Q2. The gravitational force between two bodies is:
- Always attractive
- Always repulsive
- Sometimes attractive and sometimes repulsive
- Zero if the bodies have the same mass
Q3. If the distance between two masses is doubled, the gravitational force becomes:
- Double
- Half
- One-fourth
- One-eighth
Q4. The gravitational force between two 1 kg masses placed 1 metre apart is approximately:
- 6.67 N
- 9.8 N
- 6.67 × 10⁻¹¹ N
- 9.8 × 10⁻¹¹ N
Q5. The universal gravitational constant G:
- Depends on the medium between the masses
- Depends on the masses involved
- Is the same everywhere in the universe
- Varies with altitude
Q6. Two spheres of masses M and 2M are separated by distance r. A particle of mass m is placed at the midpoint. The net gravitational force on the particle is:
- Zero
- Towards the mass M
- Towards the mass 2M
- Perpendicular to the line joining the masses
Short Answer Questions
Q7. State Newton's universal law of gravitation. Write its mathematical expression and define each term.
Q8. Three particles of equal mass m are placed at the vertices of an equilateral triangle of side a. Calculate the gravitational force on one particle due to the other two.
Q9. Why is the gravitational force between everyday objects so small that we don't notice it, while the force between Earth and us is significant?
Q10. In your school, two students of mass 50 kg each stand 1 metre apart. Calculate the gravitational force between them. Compare this with the student's weight. (G = 6.67 × 10⁻¹¹ Nm²/kg²)
Q11. The gravitational force between two bodies is 100 N when they are 1 m apart. What is the force when they are 2 m apart? What is the force when they are 0.5 m apart?
Q12. Explain why Newton's law of gravitation is called a "universal" law. Does it apply to atoms and subatomic particles?
Long Answer Questions
Q13. State and explain Newton's universal law of gravitation. Discuss its vector form. Explain how this law explains:
(i) The motion of planets around the Sun
(ii) The falling of objects on Earth
(iii) The existence of tides
Show that the law is consistent with Kepler's third law.
Q14. Three particles of masses 1 kg, 2 kg, and 3 kg are placed at the corners of an equilateral triangle of side 1 m.
(a) Calculate the gravitational force on the 1 kg mass due to the other two masses.
(b) Calculate the gravitational force on the 2 kg mass due to the other two.
(c) Calculate the gravitational force on the 3 kg mass due to the other two.
(d) Is the system in equilibrium? Explain.
(e) What would be the net gravitational force at the centre of the triangle?
Q15. Compare the gravitational force with the electrostatic force (Coulomb's law). Discuss:
(a) Similarities between the two laws
(b) Differences (nature of force, relative strength, dependence on medium)
(c) Why gravitational force dominates at astronomical scales while electromagnetic force dominates at atomic scales
(d) The significance of both being inverse-square laws
Application-Based Problems
Q16. Two spheres of masses 100 kg and 200 kg are placed with their centres 2 m apart.
(a) Calculate the gravitational force between them.
(b) Calculate the gravitational field at the midpoint between their centres.
(c) At what point between them is the gravitational field zero?
(d) If a 1 kg mass is placed at the midpoint, calculate the net force on it.
(e) What happens to the force if the spheres are placed in water? Explain.
Q17. The mass of Earth is 6 × 10²⁴ kg and the mass of the Moon is 7.4 × 10²² kg. The distance between their centres is 3.84 × 10⁸ m.
(a) Calculate the gravitational force of attraction between Earth and the Moon.
(b) Calculate the gravitational force exerted by Earth on a 70 kg astronaut on the Moon's surface. (Moon's radius = 1.74 × 10⁶ m)
(c) Calculate the point between Earth and Moon where the gravitational fields cancel out.
(d) Explain why the Moon does not fall onto Earth despite this attractive force.
Q18. In a school experiment, students measure the gravitational force between two lead spheres using a Cavendish-type apparatus. Each sphere has mass 10 kg and radius 5 cm. They are placed with their surfaces just touching.
(a) Calculate the distance between their centres.
(b) Calculate the gravitational force between them.
(c) Compare this force with the weight of a small dust particle (mass = 10⁻⁹ kg).
(d) Discuss why such a small force is difficult to measure and how Cavendish overcame this challenge.
(e) What is the significance of measuring G in understanding the universe?