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qUESTIONS

A satellite is revolving in a circular orbit at a height h from the earth surface, such that h << R where R is the radius of the earth. Assuming that the effect of earth’s atmosphere can be neglected. The minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is

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

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

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 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

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 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

In changing the state of thermodynamics from A to B state, the heat required is Q and the work done by the system is W. The change in its internal energy is

The internal energy change in a system that has absorbed 2 Kcals of heat and done 500 J of work is

A container of volume 1m³ is divided into two equal compartments by a partition. One of these compartments contains an ideal gas at 300 K. The other compartment is vacuum. The whole system is thermally isolated from its surroundings. The partition is removed, and the gas expands to occupy the whole volume of the container. Its temperature now would be

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