Gravitation practice · Medium

Determine the energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 3R.

Assertion: If value of acceleration due to gravity of a planet is lesser than earth then escape velocity from planet is lesser too.
Reason: Escape velocity just depends only on acceleration due to gravity.

Average density of the earth

A particle of mass m is moving in a horizontal circle of radius r,under a centripetal force $= \frac{k}{{{r^2}'}}\;\mathrm{where\;}k\mathrm{\;is\;a\;constant}.$

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The radius of earth is 6400 km. At what depth below the surface of earth the acceleration due to gravity decreases by 2% than on surface of earth.

Assertion: If gravitational force is proportional to $\frac{1}{\mathrm{R}^3}$ then Keplar's second law would not be affected.
Reason: For Keplar's second law, central nature of force is the only condition.

Kepler's third law states that the square of period of revolution ($T$) of a planet around the sun is proportional to the third power of average distance, $r$ between the sun and the planet i.e. ${T}^2={Kr}^3$. Here, ${K}$ is constant. If masses of the sun and the planet are ${M}$ and ${m}$ respectively, then as per Newton's law of gravitation force of attraction between them is $F=\frac{G M m}{r^2}$, where ${G}$ is gravitational constant. The relation between ${G}$ and ${K}$ is described as

If the earth rotates faster than its present speed, the weight of an object will

Radius of orbit of satellite of earth is R. Its kinetic energy is proportional to

A small satellite is in elliptical orbit around Earth as shown. If L denotes the magnitude of its angular momentum and K denotes kinetic energy

A clock S is based on oscillation of a spring and a clock P is based on pendulum motion. Both clocks run at the same rate on earth. On a planet having the same density as earth but twice the radius

If earth were to suddenly contract to half its present size, without change in its mass, the duration of the day will be

The centripetal force acting on a satellite orbiting round the earth and the gravitational force of earth acting on the satellite both equal $F$. The net force on the satellite is

For a body to escape from earth, angle at which it should be fired is?