PYQ Bank

Show that Simple Harmonic Motion can he described as the projection on its diameter of a uniform circular motion.

A book sits on a horizontal board that is undergoing simple harmonic motion with amplitude of 1\text{ m}. The coefficient of friction between the book and the board is \mu = 0.5. Find the frequency of the motion of the board at which the book is about to slip.

The case of a Simple Harmonic Progressive Wave traversing through a medium is expressed as y = 4 \times 10^{-5} \sin(600\ \pi t + \varphi) Determine

(i) amplitude of vibration of the particles.

(ii) wavelength of the sound wave and

(iii) the phase difference between the particles situated at a distance of 22\text{ cm}. (The sound velocity in the medium is 3.4 \times 10^4\text{ cm/s}).

The maximum pressure variation P that the human ear can tolerate in loud sounds is about 28\text{ nt/m}^2. Normal atmospheric pressure is about 100,000\text{ nt/m}^2. Find the corresponding maximum displacement for a soundwave in air having a frequency of 100\text{ cycles/second}. (Take velocity of sound in air as 331\text{ m/sec.} arid density of air = 1.22\text{ kg/m}^3)

Four perfect polarizing plates are stacked so that the axis of each is turned 30 clockwise with respect to the preceding plate: the last plate is crossed with the first. How much of the intensity of an incident unpolarized light is transmitted by the stack ?

Write a short note on Holography.

The equation of a one-dimensional propagating harmonic transverse wave is given by: y = 8 \sin 30\pi \left(t - \frac{x}{240}\right) \text{meter} Find the resultant wave formed by the superposition of the incident and the reflected waves from a rigid end. Also determine the amplitude of stationary waves formed at x = 2\text{ meter}. What will be the distance between consecutive nodes ?

Write a short note on Forced oscillations.

What are damped oscillations ? Obtain the differential equation for damped oscillations and write its possible solution. Explain with corresponding sketches, when there can be very heavy damping, critical damping and weak damping.

Write a short note on Holography.

A short-focus lens is used to focus a laser beam of wavelength 6328 \AA. If the beam width is comparable to the focal length of the lens, calculate the area of cross-section of the region of focus.

Explain why a two-level system is not adequate for laser operation. Draw the essential parts of a ruby laser and explain the working principle with the help of an energy level diagram.

Calculate the peak values of \vec{E} and \vec{B} for a laser beam of power 2 \times 10^{10}\text{ W} and radius 0.1 mm.

Why an extended source is necessary to see colours in a soap-film ? Non-reflecting surfaces are made by coating very thin films of a transparent material. Find the maximum thickness of such thin coatings given that \lambda = 5.5 \times 10^{-5}\text{ cm} and \mu = 5/4.

What are the essential conditions for observing the interference of light? Two coherent sources with intensity ratio 4 : 1 interfere. Find I_{\text{max}} / I_{\text{min}}.

Sodium light is incident normally upon a plane transmission grating having 5000 lines/cm. Calculate the angular separation of the D_1 and D_2 lines in the first order spectrum. As this angular separation is very sexy small, how can one magnify it 10 times ? (Given : \lambda_{v1} = 5690\text{ \AA} and \lambda_{v2} = 5896\text{ \AA})

Give Rayleigh's criterion for resolution. Why telescopes with larger objectives are better? The objective of the telescope at St. Palomer has a diameter of 5.08 m. What is the least distance on Moon which could be resolved by it? (Given distance of moon from the Earth = 3,84,000 km and \lambda = 5890\text{ \AA}).

Differentiate between Fresnel and Fraunhoffer diffractions. How can one explain the Fresnel diffraction pattern due to a straight edge?

A thin quartz plate for incident light of \lambda = 6100\ \text{\AA} produces, a phase difference (45/4)\lambda between the ordinary and extraordinary rays. What will be the nature of polarisation of the emergent light when plane polarized light of wavelength 4500\text{\AA} is incident on it.

Calculate the minimum plate separation in a Fabry-Perot interferometer to obtain free spectral range of 0.05\text{\AA} in the wave length region 5000\text{\AA}. Calculate also the smallest resolvable wavelength difference for reflectivity of 0.95.