BITSAT Gravitation — practice questions
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The value of acceleration due to gravity $g$ on tThe universal gravitational constant $G$ has the SI value approximately:
The acceleration due to gravity at height $h$ aboFor a satellite of mass $m$ orbiting Earth at radius $r$ (from the centre), the orbital velocity is:
Kepler's first law (law of orbits) states that eaThe escape velocity from the Earth's surface is approximately ($R = 6.4 \times 10^6$ m, $g = 9.8$ m/s²):The universal gravitational constant G has approximate value:Newton's law of gravitation states the force between two masses is:At the surface of Earth, acceleration due to gravity g equals:At the centre of the Earth, the value of g is:Escape velocity from Earth's surface is approximately:The first cosmic velocity (orbital velocity at Earth's surface) is approximately:At a height h above Earth's surface where h ≪ R, g' equals:At depth d below Earth's surface, g' equals:Gravitational potential energy of a mass m at the surface of Earth (taking U at infinity as zero):Time period T of a satellite in orbit of radius r around Earth is (Kepler's 3rd law):Acceleration due to gravity at the EQUATOR compared to that at the POLES:Gravitational field strength I (also called g) at distance r from a point mass M:For a satellite to be GEOSTATIONARY (stays over the same point on Earth), its orbital period must equal:Two masses 6 kg and 3 kg are 2 m apart. Gravitational force between them (G = 6.67 × 10⁻¹¹):If Earth shrinks to half its radius keeping mass constant, the new escape velocity becomes:Kepler's second law states that the line joining a planet to the sun sweeps equal areas in equal times. This iA satellite is in circular orbit at radius 2R from Earth's centre. Its orbital velocity in terms of v_surface Total energy of a satellite in circular orbit equals:Two planets orbit the same star with semi-major axes 1 AU and 4 AU. Ratio of their orbital periods T1 : T2 is:Escape velocity from a planet of mass M and radius R is v. From a planet of mass 4M and radius 2R, escape veloAt what height above Earth's surface is g reduced to half its surface value?A body falls from infinity to Earth's surface. Its velocity at the surface (in terms of escape velocity v_e):Two satellites of equal mass orbit Earth at radii r1 and r2 = 2r1. Ratio of their kinetic energies KE1 : KE2:Gravitational potential at the centre of a uniform spherical shell of mass M and radius R:A geostationary satellite orbits Earth at radius r_g. Another satellite orbits at radius r_g/4. Its period is The acceleration due to gravity on Moon (mass 1/81 Earth, radius 1/4 Earth) is approximately:Gravitational PE of a 2 kg mass at altitude 2R above Earth's surface (g at surface = 10, R = 6400 km):At what point on the line joining Earth and Moon is the net gravitational field zero? (M_E = 81 M_moon)A satellite in elliptical orbit has maximum speed v_max at perigee (closest) and minimum v_min at apogee. The Total mechanical energy of a satellite escaping Earth from low orbit at radius R is: