Orbits, Kepler's laws, gravitational potential, oscillations, springs, pendulums.
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Q1 · Gravitation & SHM · MEDIUM
A satellite of mass m orbits the Earth at a height equal to the Earth's radius R. If the satellite's orbital speed is suddenly reduced to half its value, the satellite will fall towards Earth. The maximum speed it attains just before hitting Earth's surface (neglecting atmospheric drag) is:
Q2 · Gravitation & SHM · MEDIUM
A satellite is revolving in a circular orbit of radius 2R around a planet of radius R and mean density ρ. If the satellite is to escape the gravitational field of the planet, the minimum percentage increase in its speed is:
Q3 · Gravitation & SHM · MEDIUM
A satellite is orbiting Earth in a circular orbit of radius 2R, where R is Earth's radius. If the satellite is to be transferred to a circular orbit of radius 4R, the ratio of the orbital speeds in the initial and final orbits is:
Q4 · Gravitation & SHM · MEDIUM
A satellite is in a circular orbit of radius 2R around Earth (radius R). The minimum energy required to transfer it to an orbit of radius 4R is (where M is Earth's mass):
Q5 · Gravitation & SHM · MEDIUM
A satellite of mass m orbits a planet of mass M at radius r with period T. If another satellite of mass 2m orbits the same planet at radius 2r, its orbital period will be: