Gravitation

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Q1. If the mass of the Earth were to double, what would happen to the gravitational force experienced by an object on its surface?

Solution:

Gravitational force is directly proportional to mass. If mass doubles, force also doubles.

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Q2. What is the gravitational force between two 1 kg masses placed 1 meter apart? (G = 6.67 × 10^-11 N m²/kg²)

Solution:

F = G * (m1 * m2) / r² = (6.67 × 10^-11) * (1 * 1) / (1²) = 6.67 × 10^-11 N

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Q3. Which of the following correctly describes the relationship between gravitational force and distance?

Solution:

Gravitational force is inversely proportional to the square of the distance between the centers of two masses.

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Q4. How does the gravitational force between two objects change if the mass of one object is halved?

Solution:

Gravitational force is directly proportional to the product of the masses. Halving one mass halves the force.

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Q5. What is the escape velocity from the surface of the Earth? (R = 6.4 × 10^6 m, g = 9.8 m/s²)

Solution:

Escape velocity v = √(2gR) = √(2 * 9.8 * 6.4 × 10^6) ≈ 11.2 km/s.

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Q6. What is the gravitational field strength at a distance of 10 m from a mass of 100 kg? (G = 6.67 × 10^-11 N m²/kg²)

Solution:

g = G * M / r² = (6.67 × 10^-11) * (100) / (10²) = 6.67 × 10^-10 N/kg

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Q7. If the mass of an object is tripled and the distance from the center of the Earth is halved, how does the gravitational force change?

Solution:

F ∝ m/r²; if m is tripled and r is halved, F = 3m/(1/4) = 12m, so it increases by a factor of 9.

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Q8. What is the gravitational force between two objects of mass 5 kg and 10 kg separated by a distance of 2 m? (G = 6.67 × 10^-11 N m²/kg²)

Solution:

Using the formula F = G * (m1 * m2) / r², we have F = (6.67 × 10^-11) * (5 * 10) / (2²) = 1.67 × 10^-10 N.

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Q9. If the radius of the Earth is doubled, what will happen to the gravitational force experienced by an object on its surface?

Solution:

Gravitational force is inversely proportional to the square of the radius. If radius is doubled, F becomes F/4.

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Q10. How does gravitational potential energy (U) change when the distance from the center of the Earth increases? (2020)

Solution:

Gravitational potential energy increases as the distance from the center of the Earth increases.