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qUESTIONS

A test particle is moving in a circular orbit in the gravitational field produced by a mass density ρ(r) = k/r^2 . Identify the correct relation between the radius R of the particle’s orbit and its period T

The acceleration due to gravity near the surface of a planet of radius R and density d is proportional to

What is the minimum energy required to launch a satellite of mass m from the surface of the earth of mass M and radius R in a circular orbit at an altitude of 2R

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T. then

A solid sphere of mass ‘M’ and radius ‘a’ is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance 3a from the centre will be

A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon. Assume that the density of the earth and the moon are equal, and that the earth’s volume is 64 times the volume of the moon

Four identical particles of mass M are located at the corners of a square of side ‘a’. What should be their speed if each of them revolves under the influence of others gravitational field in a circular orbit circumscribing the square

A straight rod of length L extends from x = a to x=L+a. The gravitational force it exerts on a point mass ‘m’ at x = 0 , if the mass per unit length of the rod is A+ Bx², is given by

The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2s. The period of oscillation of the same pendulum on the planet would be

Two stars of masses 3×10^31 kg each, and at distance 2 X 10^11 m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star’s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is (Take Gravitational constant G =6.67 X 10^-11Nm^2kg^-2)

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