NEET Gravitation — Set 23

Q: Is this practice set completely free?

Yes, all our chapter-wise practice sets are 100% free. You can practice as many times as you want without any hidden charges.

Q: Are these questions relevant for the latest NEET syllabus?

Absolutely. Our content team regularly updates the question bank to strictly align with the latest NTA NEET syllabus and NCERT textbooks.

Q: Can I view the solutions after the test?

Yes, once you submit the test, you will get an instant scorecard along with the correct answers and detailed explanations for every question.

Question 1

A planet moves in an elliptical orbit around the Sun with a semi-major axis of $ 2.25 \times 10^{11} \, \text{m} $. If its orbital period is 2 years, what is the mass of the Sun? (Take $ G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 $, $ 1 \, \text{year} = 3.156 \times 10^7 \, \text{s} $)

TopperSquare Expert · Accepted Answer

Using Kepler’s third law: $ T^2 = \frac{4\pi^2}{G M_s} a^3 $. Rearrange for $ M_s $: $ M_s = \frac{4\pi^2 a^3}{G T^2} $. $ T = 2 \times 3.156 \times 10^7 = 6.312 \times 10^7 \, \text{s} $. $ a = 2.25 \times 10^{11} \, \text{m} $. $ T^2 = (6.312 \times 10^7)^2 = 3.984 \times 10^{15} \, \text{s}^2 $. $ a^3 = (2.25 \times 10^{11})^3 = 1.139 \times 10^{33} \, \text{m}^3 $. $ M_s = \frac{4 \times (3.14)^2 \times 1.139 \times 10^{33}}{6.67 \times 10^{-11} \times 3.984 \times 10^{15}} $. $ M_s = \frac{4.49 \times 10^{34}}{2.657 \times 10^5} \approx 1.69 \times 10^{30} \, \text{kg} $.

Question 2

A planet orbits the Sun with a period of 10 years. If Earth’s orbital radius is $ 1.5 \times 10^{11} \, \text{m} $, what is its semi-major axis?

TopperSquare Expert · Accepted Answer

Kepler’s third law: $ \frac{T_p^2}{T_E^2} = \frac{a_p^3}{a_E^3} $. $ T_E = 1 \, \text{year} $, $ T_p = 10 \, \text{years} $, $ a_E = 1.5 \times 10^{11} \, \text{m} $. $ \frac{10^2}{1^2} = \frac{a_p^3}{(1.5 \times 10^{11})^3} $. $ 100 = \frac{a_p^3}{3.375 \times 10^{33}} $. $ a_p^3 = 100 \times 3.375 \times 10^{33} = 3.375 \times 10^{35} $. $ a_p = (3.375 \times 10^{35})^{1/3} \approx 6.96 \times 10^{11} \, \text{m} $.

Question 3

Three masses of $ 4 \, \text{kg} $ each are at the vertices of an equilateral triangle with side $ 3 \, \text{m} $. What is the net force on one mass? ($ G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 $)

TopperSquare Expert · Accepted Answer

Force between two masses: $ F = G \frac{m_1 m_2}{r^2} = 6.67 \times 10^{-11} \frac{4 \times 4}{3^2} = 1.185 \times 10^{-10} \, \text{N} $. Two forces act at 60°: $ F_R = \sqrt{F^2 + F^2 + 2 F^2 \cos 60^\circ} $. $ F_R = \sqrt{(1.185 \times 10^{-10})^2 (1 + 1 + 1)} = 1.185 \times 10^{-10} \sqrt{3} $. $ F_R \approx 2.05 \times 10^{-10} \, \text{N} $.

NEET Physics — Gravitation

Accelerate Your NEET Preparation

Question Bank

Practice Tests

NEET PYQs

AI Analytics

About this NEET MCQ Test

Preview of Questions in this Test

Q2. A planet orbits the Sun with a period of 10 years. If Earth’s orbital radius is \( 1.5 \times 10^{11} \, \text{m} \), what is its semi-major axis?

Q3. Three masses of \( 4 \, \text{kg} \) each are at the vertices of an equilateral triangle with side \( 3 \, \text{m} \). What is the net force on one mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q4. A satellite near Earth has a period of 86 minutes. What is its period at \( h = 5 R_E \)? (\( R_E = 6.4 \times 10^6 \, \text{m} \))

Q5. What is the primary source of centripetal force for an Earth satellite?

Frequently Asked Questions

Is this practice set completely free?

Are these questions relevant for the latest NEET syllabus?

Can I view the solutions after the test?

About TopperSquare

More Physics Chapters for NEET

Explore More NEET Subjects

Everything you need to crack NEET

NEET Physics: Gravitation — MCQ Test 23

Q6. What is the kinetic energy of a \( 150 \, \text{kg} \) satellite at \( 3 R_E \) from Earth’s center? (\( M_E = 6 \times 10^{24} \, \text{kg}, R_E = 6.4 \times 10^6 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q7. What is the escape speed from a planet with mass \( 1.8 \times 10^{24} \, \text{kg} \) and radius \( 3.5 \times 10^6 \, \text{m} \)? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q8. What condition must an object’s energy satisfy to remain bound to Earth?

Q9. What is the kinetic energy of a \( 500 \, \text{kg} \) satellite at \( 7 R_E \) from Earth’s center? (\( M_E = 6 \times 10^{24} \, \text{kg}, R_E = 6.4 \times 10^6 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q10. What does the negative total energy of a bound system indicate?