Gravitation
Physics ⇒ Mechanics
Gravitation starts at 9 and continues till grade 12.
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See sample questions for grade 12
A body is dropped from a height h above the surface of the Earth, where h is much smaller than the radius of the Earth. Derive the expression for the time taken to reach the ground, considering the variation of g with height.
A comet moves in a highly elliptical orbit around the Sun. At which position in its orbit does it have the maximum kinetic energy? Explain your answer.
A planet has a mass 8 times that of Earth and a radius 2 times that of Earth. What will be the acceleration due to gravity on its surface compared to that on Earth?
A planet orbits a star in an elliptical orbit with the star at one focus. If the planet is closest to the star at point A and farthest at point B, compare the speeds of the planet at points A and B. Justify your answer using the law of conservation of angular momentum.
A satellite of mass m is in a circular orbit of radius r around a planet of mass M. Derive an expression for the orbital speed of the satellite and show how it depends on the mass of the planet and the radius of the orbit.
If the gravitational force between two objects is F and the distance between them is increased by a factor of 3, what will be the new force between them?
A body is projected vertically upwards from the surface of the Earth with a velocity equal to the escape velocity. What will be its velocity when it is infinitely far from the Earth?
A body of mass 10 kg is taken to a height equal to the radius of the Earth above its surface. What is its weight at that height? (Take g = 9.8 m/s^2)
A mass m is placed at a distance r from another mass M. Write the expression for the gravitational force between them.
A planet has twice the mass of Earth and the same radius. What is the escape velocity from its surface compared to that of Earth?
A satellite is orbiting the Earth at a height where the acceleration due to gravity is 4.9 m/s^2. If the radius of the Earth is 6,400 km, what is the height of the satellite above the Earth's surface?
A satellite is revolving around the Earth in a circular orbit. What provides the necessary centripetal force for its motion?
Describe the difference between gravitational mass and inertial mass.
Explain why astronauts feel weightless inside an orbiting spacecraft.
If the distance between two masses is reduced to half, by what factor does the gravitational force between them change?
If the mass of a planet is doubled and its radius is halved, how does the acceleration due to gravity at its surface change?
If the mass of the Earth is 6 \times 10^{24} kg and its radius is 6.4 \times 10^6 m, calculate the acceleration due to gravity at the surface of the Earth.
If the mass of the Earth were to increase by 10% with no change in its radius, how would the value of g at the surface change?
State Kepler's three laws of planetary motion.
State Newton's law of universal gravitation.
