Gravitation

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Q1. What is the gravitational force between two objects of mass m1 and m2 separated by a distance r? (2021)

Solution:

The gravitational force is given by Newton's law of gravitation: F = G * (m1 * m2) / r^2.

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Q2. If the radius of the Earth were to increase while keeping its mass constant, what would happen to the gravitational acceleration at its surface?

Solution:

Gravitational acceleration g = GM/R². If R increases, g decreases.

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Q3. What is the gravitational field strength at a distance of 3R from the center of the Earth? (R = radius of the Earth) (2022)

Solution:

Gravitational field strength decreases with the square of the distance. At 3R, it is g/9.

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Q4. What is the escape velocity from the surface of a planet with a radius of 4,000 km and a mass of 6 × 10^24 kg? (G = 6.67 × 10^-11 N m²/kg²)

Solution:

Escape velocity = √(2GM/R) = √(2 * 6.67 × 10^-11 * 6 × 10^24 / 4 × 10^6) = 11,200 m/s

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Q5. Calculate the weight of a 10 kg object on the surface of the Earth (g = 9.8 m/s²).

Solution:

Weight W = m * g = 10 kg * 9.8 m/s² = 98 N.

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Q6. 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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Q7. Calculate the weight of a 10 kg object on the surface of Mars, where the acceleration due to gravity is 3.7 m/s².

Solution:

Weight = mass * gravity = 10 kg * 3.7 m/s² = 37 N

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Q8. 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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Q9. 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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Q10. If the gravitational force between two objects is 20 N and the distance between them is doubled, what will be the new force?

Solution:

F is inversely proportional to r². If r is doubled, F becomes F/4 = 20 N / 4 = 5 N.