No part of India is situated on the equator. Is it possible to have a geostationary satellilte which always remains over New Delhi?

String I and II have identical and linear mass densities, but string I is under greater tension than string II . The accompanying figure shows four different situations, A to D , in which standing wave patterns exist on the two strings. In which situation it is possible that strings I and II are oscillating at the same resonant frequency ?

An electromagnetic wave can be represented by E = A sin (kx- omega t + phi) , where E is electric field associated with wave, According this equation, for any value of x, E remains sinusoidal for -oolt t lt oo . Obviously this corresponds to an idealised situation because radiation from ordinary sources consists of finite size wavetrains. In general, electric field remains sinusoidal only for times of order tau_(c) ' which is called coherence time. In simpler language it means that for times of order tau_(c)' a wave will have a definite phase. The finite value of coherence time could be due to many factors, for example if radiating atom undergoes collision with another atom then wave train undergoes an abrupt phase change or due to the fact that an atom responsible for emitting radiation has a finite life time in the energy level from which it drops to lower energy level, while radiating. Concept of coherence time can be easily understood using young's double slit experiment. Let interference patten is observed around point P at time t , due to superposition of waves emanting from S_(1) and S_(2) at times t =(r_(1))/(c) and (r_(2))/(c) respectively, where r_(1) and r_(2) are the distances S_(1) P & S_(2)P . Obviously if (r_(2)-r_(1))/(c) lt lt tau_(e),{"where" " "c = 3xx10^(8)m//s} then, wavetrain arriving at point P from S_(1) & S_(2) will have a definite phase relationship and an interference pattern of good contranst will be obtained. If coherence time is of order 10^(-10) second and screen is placed at a very large distance from slits in the given figure, then:-

An electromagnetic wave can be represented by E = A sin (kx- omega t + phi) , where E is electric field associated with wave, According this equation, for any value of x, E remains sinusoidal for -oolt t lt oo . Obviously this corresponds to an idealised situation because radiation from ordinary sources consists of finite size wavetrains. In general, electric field remains sinusoidal only for times of order tau_(c) ' which is called coherence time. In simpler language it means that for times of order tau_(c)' a wave will have a definite phase. The finite value of coherence time could be due to many factors, for example if radiating atom undergoes collision with another atom then wave train undergoes an abrupt phase change or due to the fact that an atom responsible for emitting radiation has a finite life time in the energy level from which it drops to lower energy level, while radiating. Concept of coherence time can be easily understood using young's double slit experiment. Let interference patten is observed around point P at time t , due to superposition of waves emanting from S_(1) and S_(2) at times t =(r_(1))/(c) and (r_(2))/(c) respectively, where r_(1) and r_(2) are the distances S_(1) P & S_(2)P . Obviously if (r_(2)-r_(1))/(c) lt lt tau_(e),{"where" " "c = 3xx10^(8)m//s} then, wavetrain arriving at point P from S_(1) & S_(2) will have a definite phase relationship and an interference pattern of good contranst will be obtained. If coherence time is of order 10^(-10) second and screen is placed at a very large distance from slits in the given figure, then:-

Huygen was the figure scientist who proposed the idea of wave theory of light he said that the light propagates in form of wavelengths. A wavefront is a imaginary surface of every point of which waves are in the same. phase. For example the wavefront for a point source of light is collection of concentric spheres which have centre at the origin w_(1) is a wavefront w_(2) is another wavefront. The radius of the wavefront at time 't' is 'ct' in thic case where 'c' is the speed of light the direction of propagation of light is perpendicular to the surface of the wavelength. the wavefronts are plane wavefronts in case of a parallel beam of light. Huygen also said that every point of the wavefront acts as the source of secondary wavelets. The tangent drawn to all secondary wavelets at a time is the new wavefront at that time. The wavelets are to be considered only in the forward direction (i.e., the direction of propagation of light) and not in the reverse direction if a wavefront w_(1) and draw spheres of radius 'cDeltat' they are called secondary wavelets. Draw a surface w_(2) which is tangential to all these secondary wavelets w_(2) is the wavefront at time t+Deltat Huygen proved the laws of reflection and laws of refraction using concept of wavefront. Q. A point source of light is placed at origin, in air. the equation of wavefront of the wave at time t, emitted by source at t=0 is (take refractive index of air as 1)

The vividh Bharati station of All india Radio Delhi . Broadcasts on a frequency of 1.368 kHz (kilo hertz) Calculate the wavelength of the elctromagnetic radiation emitted by transmitter .Which part of the electromagnetic spectrum does it belong to ?

Which of the following statement is true for variation in organisms? (1) The occurrence of differences among the individuals of the same species is known as variation. (2) Variations decrease the possibilities of survival. (3) The process of evolution decreases the variation in organisms. ( 4) During meiosis, crossing over takes place between the genes and hence, new combinations are formed, which ultimately results in producing variations.

A circus wishes to develop a new clown act. Fig. (1) shows a diagram of the proposed setup. A clown will be shot out of a cannot with velocity v_(0) at a trajectory that makes an angle theta=45^(@) with the ground. At this angile, the clown will travell a maximum horizontal distance. The cannot will accelerate the clown by applying a constant force of 10, 000N over a very short time of 0.24s . The height above the ground at which the clown begins his trajectory is 10m . A large hoop is to be suspended from the celling by a massless cable at just the right place so that the clown will be able to dive through it when he reaches a maximum height above the ground. After passing through the hoop he will then continue on his trajectory until arriving at the safety net. Fig (2) shows a graph of the vertical component of the clown's velocity as a function of time between the cannon and the hoop. Since the velocity depends on the mass of the particular clown performing the act, the graph shows data for serveral different masses. If the angle the cannot makes with the horiaontal is increased from 45^(@) , the hoop will have to be

A circus wishes to develop a new clown act. Fig. (1) shows a diagram of the proposed setup. A clown will be shot out of a cannot with velocity v_(0) at a trajectory that makes an angle theta=45^(@) with the ground. At this angile, the clown will travell a maximum horizontal distance. The cannot will accelerate the clown by applying a constant force of 10, 000N over a very short time of 0.24s . The height above the ground at which the clown begins his trajectory is 10m . A large hoop is to be suspended from the celling by a massless cable at just the right place so that the clown will be able to dive through it when he reaches a maximum height above the ground. After passing through the hoop he will then continue on his trajectory until arriving at the safety net. Fig (2) shows a graph of the vertical component of the clown's velocity as a function of time between the cannon and the hoop. Since the velocity depends on the mass of the particular clown performing the act, the graph shows data for serveral different masses. If the clown's mass is 80 kg , what initial velocity v_(0) will have as he leaves the cannot?

The ciliary muscles of eye control the curvature of the lens in the eye and hence can alter the effective focal length of the system. When the muscles are fully relaxed, the focal length is maximum. When the muscles are strained, the curvature of lens increases. That means radius of curvature decreases and focal length decreases. For a clear vision, the image must be on the retina. The image distance is therefore fixed for clear vision and it equals the distance of retina from eye lens. It is about 2.5cm for a grown up person. A perosn can theoretically have clear vision of an object situated at any large distance from the eye. The smallest distance at which a person can clearly see is related to minimum possible focal length. The ciliary muscles are most strained in this position. For an average grown up person, minimum distance of the object should be around 25cm. A person suffering from eye defects uses spectacles (eye glass). The function of lens of spectacles is to form the image of the objects within the range in which the person can see clearly. The image o the spectacle lens becomes object for the eye lens and whose image is formed on the retina. The number of spectacle lens used for th eremedy of eye defect is decided by the power fo the lens required and the number of spectacle lens is equal to the numerical value of the power of lens with sign. For example, if power of the lens required is +3D (converging lens of focal length 100//3cm ), then number of lens will be +3 . For all the calculations required, you can use the lens formula and lensmaker's formula. Assume that the eye lens is equiconvex lens. Neglect the distance between the eye lens and the spectacle lens. Q. Maximum focal length of a eye lens of a normal person is