Assertion A: Ignoring air resistance and the Earth's rotation, the escape speed from the Earth's surface is the same for every launch direction. Reason R: The orbital speed of a satellite in a given orbit does not depend on the mass of the satellite. Choose the correct answer.

Both A and R are correct but R is not the correct explanation of A

A is not correct but R is correct

Both A and R are correct and R is the correct explanation of A

A is correct but R is not correct

Given below are two statements: Statement I: The orbital speed of a satellite close to the Earth's surface is 1/√2 times the escape speed from the surface. Statement II: A heavier projectile needs a larger escape speed from the Earth than a lighter one. Choose the correct answer.

Statement I is correct but Statement II is incorrect

Statement I is incorrect but Statement II is correct

Both Statement I and Statement II are incorrect

Both Statement I and Statement II are correct

Gravitation

10 NEET-UG practice questions on Gravitation, part of Physics. The first 10 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

Question 1 · Medium
Assertion A: Ignoring air resistance and the Earth's rotation, the escape speed from the Earth's surface is the same for every launch direction. Reason R: The orbital speed of a satellite in a given orbit does not depend on the mass of the satellite. Choose the correct answer.
1. ABoth A and R are correct but R is not the correct explanation of A
2. BA is not correct but R is correct
3. CBoth A and R are correct and R is the correct explanation of A
4. DA is correct but R is not correct
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Answer: A · Both A and R are correct but R is not the correct explanation of A
Escape needs (1/2)mv² = GMm/R; energy is a scalar, so the direction of launch does not enter. Orbital speed √(GM/r) has no satellite mass in it, so R is also true. But R concerns orbital motion and does not explain why direction is irrelevant to escape.
- B: A is correct, since the energy condition has no direction in it.
- C: R is true but is about mass in an orbit, not about launch direction.
- D: R is a correct statement, since m cancels in the force balance.
Remember this
Escape speed √(2gR) depends only on the planet; neither the projectile's mass nor its direction appears.
Question 2 · Medium
An object weighs 72 N on the Earth's surface. What is its weight at a height R/2 above the surface, where R is the radius of the Earth?
1. A48 N
2. B36 N
3. C18 N
4. D32 N
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Answer: D · 32 N
Distance from the centre = 3R/2, so g' = g/(3/2)² = 4g/9. Weight = 72 × 4/9 = 32 N.
- A: This uses an inverse first power of the distance.
- B: This uses the depth formula, 1 − h/R.
- C: This takes the distance from the centre as 2R.
Remember this
Use g' = g/(1 + h/R)² when h is comparable to R; the approximation 1 − 2h/R then fails.
Question 3 · Hard
A 400 kg satellite circles the Earth at an orbital radius of 2R. How much energy must be supplied to shift it to a circular orbit of radius 4R? Take R = 6400 km and g = 10 m/s² at the surface.
1. A1.6 × 10⁹ J
2. B3.2 × 10⁹ J
3. C5.12 × 10¹⁰ J
4. D6.4 × 10⁹ J
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Answer: B · 3.2 × 10⁹ J
Total energy in an orbit of radius r is E = −GMm/(2r) = −mgR²/(2r). So E₁ = −mgR/4 and E₂ = −mgR/8, and the energy needed is mgR/8. Numerically, 400 × 10 × 6.4 × 10⁶/8 = 3.2 × 10⁹ J.
- A: This uses −GMm/(4r) for the total energy, half the correct value.
- C: This uses mgh with h = 2R, taking g as constant.
- D: This counts only the change in potential energy, ignoring the fall in kinetic energy.
Remember this
Moving a satellite outward takes ΔE = (GMm/2)(1/r₁ − 1/r₂), half the rise in potential energy.
Question 4 · Medium
Given below are two statements: Statement I: The orbital speed of a satellite close to the Earth's surface is 1/√2 times the escape speed from the surface. Statement II: A heavier projectile needs a larger escape speed from the Earth than a lighter one. Choose the correct answer.
1. AStatement I is incorrect but Statement II is correct
2. BBoth Statement I and Statement II are incorrect
3. CStatement I is correct but Statement II is incorrect
4. DBoth Statement I and Statement II are correct
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Answer: C · Statement I is correct but Statement II is incorrect
Near the surface, v₀ = √(gR) and vₑ = √(2gR), so v₀ = vₑ/√2 and Statement I holds. The mass of the projectile cancels in the energy condition, so the escape speed is the same for all masses and Statement II fails.
- A: This reverses the two truth values.
- B: Statement I is right, since vₑ = √2 v₀.
- D: Statement II is wrong, as mass cancels in the energy condition.
Remember this
A heavier body needs more escape energy, but exactly the same escape speed.
Question 5 · Easy
Treating the Earth as a sphere of uniform density, what is the acceleration due to gravity at its centre, if its value at the surface is g?
1. AZero
2. Bg/4
3. C2g
4. Dg/2
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Answer: A · Zero
Inside a uniform Earth, g at depth d is g(1 − d/R). At the centre, d = R, so the value is zero.
- B: This is the value at a height R above the surface, not at the centre.
- C: This wrongly assumes g grows on going deeper.
- D: This is the value at depth R/2, not at the centre.
Remember this
Below the surface g falls linearly to zero at the centre; above it g falls as 1/r².
Question 6 · Easy
Kepler's law of areas, for a planet going round the Sun, follows from the conservation of which quantity?
1. AKinetic energy
2. BPotential energy
3. CLinear momentum
4. DAngular momentum
Answer and explanation in LearnFree account
Question 7 · Easy
A planet's elliptical orbit around the Sun is drawn with four marked positions. At which position is its orbital speed greatest?
Figure: MedExams
1. APosition T
2. BPosition R
3. CPosition Q
4. DPosition P
Answer and explanation in LearnFree account
Question 8 · Medium
Earth is treated as a sphere of radius R and uniform density. Variation of the acceleration due to gravity g with distance r from its centre, gₛ being the surface value, is correctly shown by which graph?
Figure: MedExams
1. AGraph B
2. BGraph C
3. CGraph A
4. DGraph D
Answer and explanation in LearnFree account
Question 9 · Hard
A satellite of mass m is shifted from Orbit 1 to Orbit 2 around a planet of radius R, where surface gravity is g. The drawing marks heights above the surface. What minimum energy is needed for the shift?
Figure: MedExams
1. AmgR
2. BmgR/12
3. CmgR/4
4. DmgR/6
Answer and explanation in LearnFree account
Question 10 · Medium
Two satellites move in the circular orbits drawn around one planet, A having a period of 3 h. What are the period of B and the ratio of orbital speed of A to that of B?
Figure: MedExams
1. A24 h and 1/2
2. B48 h and 4
3. C24 h and 2
4. D12 h and 2
Answer and explanation in LearnFree account

Gravitation

Assertion A: Ignoring air resistance and the Earth's rotation, the escape speed from the Earth's surface is the same for every launch direction. Reason R: The orbital speed of a satellite in a given orbit does not depend on the mass of the satellite. Choose the correct answer.

An object weighs 72 N on the Earth's surface. What is its weight at a height R/2 above the surface, where R is the radius of the Earth?

A 400 kg satellite circles the Earth at an orbital radius of 2R. How much energy must be supplied to shift it to a circular orbit of radius 4R? Take R = 6400 km and g = 10 m/s² at the surface.

Given below are two statements: Statement I: The orbital speed of a satellite close to the Earth's surface is 1/√2 times the escape speed from the surface. Statement II: A heavier projectile needs a larger escape speed from the Earth than a lighter one. Choose the correct answer.

Treating the Earth as a sphere of uniform density, what is the acceleration due to gravity at its centre, if its value at the surface is g?

Kepler's law of areas, for a planet going round the Sun, follows from the conservation of which quantity?

A planet's elliptical orbit around the Sun is drawn with four marked positions. At which position is its orbital speed greatest?

Earth is treated as a sphere of radius R and uniform density. Variation of the acceleration due to gravity g with distance r from its centre, gₛ being the surface value, is correctly shown by which graph?

A satellite of mass m is shifted from Orbit 1 to Orbit 2 around a planet of radius R, where surface gravity is g. The drawing marks heights above the surface. What minimum energy is needed for the shift?

Two satellites move in the circular orbits drawn around one planet, A having a period of 3 h. What are the period of B and the ratio of orbital speed of A to that of B?