Gravitational Constant G - UNSOLVED PRACTICE SET

Q7. What is the significance of the gravitational constant G? Why is it called a "universal" constant?

Q8. Describe the basic principle of Cavendish's experiment to determine G.

Q9. Given G = 6.67 × 10⁻¹¹ Nm²/kg², g = 9.8 m/s², and Earth's radius R = 6.4 × 10⁶ m, calculate the mass of the Earth.

Q10. In your school physics lab, why can't you measure G using ordinary spring balances and standard masses? What makes G so difficult to measure?

Q11. The gravitational force between two 100 kg spheres placed 1 m apart is F. Calculate F and explain why this force is too small to feel.

Q12. How does the knowledge of G help us determine the mass of the Sun? Write the basic relation used.n here...

Q13. Describe Cavendish's experiment to determine the value of G. Explain:

(i) The apparatus used (torsion balance)

(ii) The principle behind the experiment

(iii) Why the setup needs to be extremely sensitive

(iv) How the result can be used to find the mass and density of the Earth

(v) The significance of this experiment in the history of physics

Q14. Discuss the properties of gravitational constant G:

(a) Its dimensional formula

(b) Its value in different systems of units (SI and CGS)

(c) Why it is the weakest fundamental force constant

(d) Why it is so difficult to measure precisely

(e) Current challenges in determining its exact value

(f) The significance of G in cosmology and astrophysics

Q15. A student proposes an experiment to measure G using two 1 kg masses and a sensitive electronic balance.

(a) Calculate the gravitational force between the masses when placed 10 cm apart.

(b) If the balance can detect 10⁻⁶ N, can it measure this force?

(c) What modifications would you suggest to make the measurement feasible?

(d) Discuss the sources of error in such an experiment.

(e) Why do modern experiments use much larger masses and more sophisticated techniques?

Q16. The mass of the Sun is 2 × 10³⁰ kg and the orbital radius of Earth is 1.5 × 10¹¹ m.

(a) Using Kepler's third law and the value of G, verify the orbital period of Earth (365 days).

(b) If G were 10% larger, how would Earth's orbital period change?

(c) Calculate the gravitational force between the Sun and Earth.

(d) Calculate the centripetal force required to keep Earth in orbit and verify that it equals the gravitational force.

(e) Discuss how astronomers use G to determine the mass of distant stars.

Q17. In a Cavendish-type experiment, two small spheres of mass 10 g each are attached to a light rod of length 20 cm. The rod is suspended by a thin fibre. Two large spheres of mass 10 kg each are brought near the small spheres.

(a) Calculate the gravitational force between one small sphere and one large sphere when their centres are 5 cm apart.

(b) Calculate the torque on the suspended system due to this force.

(c) If the fibre twists by 0.5° and the torsion constant is 10⁻⁸ Nm/rad, calculate the angle of twist in radians.

(d) Using the relation τ = kθ, verify if the measured twist is consistent with the calculated torque.

(e) Discuss how this experiment can be improved for better accuracy.

Q18. A student reads that the latest measurement of G gives (6.67430 ± 0.00015) × 10⁻¹¹ Nm²/kg².

(a) What does the uncertainty ± 0.00015 tell us about the precision of the measurement?

(b) Calculate the percentage uncertainty.

(c) If you use this value to calculate Earth's mass, what is the uncertainty in the result?

(d) Why is G the least precisely known fundamental constant?

(e) Discuss how improvements in measuring G could impact our understanding of gravity.