A test particle is moving in a circular orbit in the gravitational field produced by a mass density \rho (r) = {K \over {{r^2}}} . Identify the correct relation between the radius R of the particle's orbit and its period T

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 other's gravitational field in a circular orbit circumscribing the square?

A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will 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 :

A satellite is revolving in a circular orbit at a height h form the earth surface, such that h < < R where R is 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 :

Two stars of masses 3 $$\times$$ 1031 kg each, and at distance 2 $$\times$$ 1011 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 $$\times$$ 10–11 Nm2 kg–2)

A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is -

The energy required to take a satellite to a height 'h' above Earth surface (radius of Earth = 6.4 $$\times$$ 103 km) is E1 and kinetic energy required for the satellite to be in a circular orbit at this height is E2. The value of h for which E1 and E2 are equal, is

In a Young's double slit experiment, the ratio of the slit's width is 4 : 1. The ratio of the intensity of maxima to minima, close to the central fringe on the screen, will be :

A system of three polarizers P1, P2, P3 is set up such that the pass axis of P3 is crossed with respect to that of P1. The pass axis of P2 is inclined at 60o to the pass axis of P3. When a beam of unpolarized light of intensity I0 is incident on P1, the intensity of light transmitted by the three polarizers is I. The ratio ({{{I_0}} \over I}) equals (nearly) :

In a double slit experiment, when a thin film of thickness t having refractive index $$\mu$$. is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of t is ($$\lambda$$ is the wavelength of the light used) :

The value of numerical aperature of the objective lens of a microscope is 1.25. If light of wavelength 5000 $$\stackrel{o}{A}$$ is used, the minimum separation between two points, to be seen as distinct, will be :

Diameter of the objective lens of a telescope is 250 cm. For light of wavelength 600nm. coming from a distant object, the limit of resolution of the telescope is close to :-

The figure shows a Young's double slit experimental setup. It is observed that when a thin transparent sheet of thickness t and refractive index μ is put in front of one of the slits, the central maximum gest shifted by a distance equal to n fringe widths. If the wavelength of light used is $$\lambda$$, t will be :

Calculate the limit of resolution of a telescope objective having a diameter of 200 cm, if it has to detect light of wavelength 500 nm coming from a star :-

In a double-slit experiment, green light (5303$$\stackrel{\circ }{A}$$) falls on a double slit having a separation of 19.44 $$\mu$$m and awidht of 4.05 $$\mu$$m. The number of bright fringes between the first and the second diffraction minima is :

In a Young's double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is {1 \over 8} th of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to :

Consider a Young’s double slit experiment as shown in figure. What should be the slit separation d in terms of wavelength $$\lambda$$ such that the first minima occurs directly in front of the slit (S1) ?