Parra QkAS ul O7 = ChatGPT Cn ¢ Important Theory / Derivation Questions 1. State and explain Newton’s law of gravitation. Why is it called an inverse-square law? 2. Derive the expression for acceleration due to gravity (g) at the surface of ladon 3. Derive the expression for g at a height h above the Earth's surface. 4. Derive the expression for g at a depth d below the Earth’s surface. 5. Show that the value of g ata depth d is given by ga = g(1 — 4). 6. Derive the expression for orbital velocity of a satellite. 7. Derive the expression for time period of revolution of a satellite (Kepler’s third law). @) Ask anything g a)21:21 10. nF vz irs ce soy AT 7a ») alk ChatGPT Cn Derive the expression for escape velocity of Earth. Why is escape velocity independent of the mass of the body? Distinguish between geostationary and polar satellites. Give two applications of each. State Kepler's laws of planetary motion and explain them. Derive the expression for variation of g with latitude (due to Earth’s rotation). What is gravitational potential energy? Derive its expression for a body of mass m at a distance r from Earth’s center. Define gravitational potential and derive an expression for it at a distance r from a mass M. Define gravitational field intensity and derive its relation with potential. ray an Sl aeeTanzaliaye) g a)Parva QkhkACua &7 = ChatGPT BG: and polar satellites. Give two applications of each. 11. State Kepler’s laws of planetary motion and explain them. 12. Derive the expression for variation of g with latitude (due to Earth's rotation). 13. What is gravitational potential energy? Derive its expression for a body of mass m at a distance r from Earth’s center. 14. Define gravitational potential and derive an expression for it at a distance r from a mass M. 15. Define gravitational field intensity and derive its relation with potential. 16. Explain the concept of weightlessness in a satellite. NY @ Evnartad Canrantisal ray an Sl aeeTanzaliaye) g Pt)Parva QkhkACua &7 = ChatGPT Cn ¢ Expected Conceptual Short Questions 1. Why is g maximum at poles and minimum at equator? 2. Why does the value of g decrease with height and depth? 3. Why is there no atmosphere on the Moon though escape velocity on the Moon is less than that of Earth? 4. Why do astronauts feel weightless in a spacecraft orbiting Earth? 5. Why does a satellite not fall into Earth though it is under Earth’s gravity? 6. Why do communication satellites have to be placed in geostationary orbits? 7. How does the mass of Earth vary if radius remains the same but g decreases? 8. Ifradius of Ear VV inks by half, kaaninn mass same what hannens to @) Ask anything g Pt)21:21 Ce eee yd = ChatGPT Cn 5. Why does a satellite not fall into Earth though it is under Earth’s gravity? 6. Why do communication satellites have to be placed in geostationary orbits? 7. How does the mass of Earth vary if radius remains the same but g decreases? 8. If radius of Earth shrinks by half, keeping mass same, what happens to escape velocity? 9. What would be the effect on orbital velocity if the satellite is placed at higher orbit? 10. Why can’t geostationary satellites be used for studying polar regions? ¢ Important Numericals ‘SL Arora by aNd 9) v ray an Sl aeeTanzaliaye) g Pt)21:22 Ce eee yd = ChatGPT Cn 1. The mass of Earth is 6 x 1074, kg and its radius is 6.4 x 108, m. Find acceleration due to gravity at the ld te lean 2. Calculate the value of g at a height of 1000 km above Earth’s surface. (Take R=6.4 x 10°, m). 3. Find the value of g at a depth of 1600 km below the Earth's surface. 4. Asatellite revolves around Earth ina circular orbit of radius 7 x 10°, m. Calculate its orbital velocity. 5. A satellite is orbiting Earth at a height of 600 km. Find its time period of revolution. 6. Calculate the escape velocity from Earth’s surface (R = al ee ee eevee 7. Calculate the escape velocity from the Moon's surface. (Radius = ACS ae eRe Tie 8. A bodv is weighed at poles and at ray an Sl aeeTanzaliaye) g Pt)21:22 QkhkACua &7 = ChatGPT Cn 8. A body is weighed at poles and at equator. If Earth’s angular velocity is 7.27 x 10-°, rad/s, calculate the difference in apparent weight of a body of mass 50 kg. 9. Acommunication satellite is revolving around Earth. If its orbital period is 24 h, find the radius of its orbit. 10. A body of mass 2 kg is raised to a height of 500 km above Earth's surface. Calculate: * (i) Potential energy at this height * (ii) Change in potential energy 11. Two bodies of masses 10 kg and 20 kg are separated by 10 m. Calculate the force of gravitation between them. 12. A geostationary satellite is orbiting Earth. Calculate its orbital velocity. 13. The mass of Mars is 6.46 x 107, kg ETRE lee eas ane aaTe ray an Sl aeeTanzaliaye) g Pt)aT a ») Phiyy atl = ChatGPT Cn 11. Two bodies of masses 10 kg and 20 kg are separated by 10 m. Calculate the force of gravitation between them. 12. A geostationary satellite is orbiting Earth. Calculate its orbital velocity. 13. The mass of Mars is 6.46 x 107°, kg and its radius is 3.39 x 10°, m. Find the acceleration due to gravity and escape velocity on Mars. 14. If g on Earth decreases by 0.5%, find the change in radius of Earth assuming its mass remains constant. 15. A projectile is fired vertically upwards with a velocity of 11.2 km/s. Will it fall back to Earth? Justify. WH These theory + conceptual + numerical questions cover all important exam points. W@W Numericals are $. .cora style - most @) Ask anything g Pt)