UPSC Physics Optional PYQs (CSE & IFoS)PYQs

In He-Ne laser, what is the function of He gas? Explain the answer with the help of energy level diagram for He – Ne laser.

Newton's rings are observed between a spherical surface of radius of curvature 100 cm and a plane glass plate. The diameters of 4th and 15th bright rings are 0.314 cm and 0.574 cm, respectively. Calculate the diameters of 24th and 36th bright rings and also the wavelength of light used.

Show that the mean kinetic and potential energies of non-dissipative simple harmonic vibrating systems are equal.

Discuss the phenomenon of Fraunhofer diffraction at a single slit and show that the intensities of successive maxima are nearly in the ratio 1 : \frac{4}{9\pi^2} : \frac{4}{25\pi^2} : \frac{4}{49\pi^2}.

Obtain the system matrix for a thick lens and derive the thin lens formula.

Two spaceships approach each other, both moving with same speed as measured by a stationary observer on the Earth. Their relative speed is 0.7c. Determine the velocity of each spaceship as measured by the stationary observer on the Earth.

A particle P of mass m_1 collides with another particle Q of mass m_2 at rest. The particles P and Q travel at angles \theta and \phi, respectively, with respect to the initial direction of P. Derive the expression for the maximum value of \theta.

Consider two frames of reference S and S' having a common origin O. The frame S' is rotating with respect to the fixed frame S with a uniform \vec{\omega}=3a_x\,\mathrm{rad\,s^{-1}}. A projectile of unit mass at position vector \vec{r}=7a_x+4a_y\,\mathrm{m} is moving with \vec{v}=14a_y\,\mathrm{m\,s^{-1}}. Calculate in the rotating frame S' the following forces on the projectile:

(i) Euler's force

(ii) Coriolis force

(iii) Centrifugal force

Show that for very small velocity, the equation for kinetic energy, K=\Delta mc^2 becomes K=\dfrac{1}{2}m_0v^2, where notations have their usual meanings.

Consider the diagram below with a water flow rate Q. Derive the expression for Q in terms of the difference in the manometer heights h and the cross-section areas A_1 and A_2:

Define moment of inertia and radius of gyration of a body of mass M rotating about an axis. State and prove Parallel Axis theorem on moment of inertia.

A solid contains a dilute concentration of \mathrm{Nd}^{3+} ions, each of which possess three 4f electrons. Assuming that there are 10^{25}\ \mathrm{m}^{-3} of these ions, calculate the magnetic susceptibility of the sample at 1\,\mathrm{K}.

An n-p-n transistor with \beta = 49 is used in common-emitter amplifier mode with V_{cc} = 10\ \mathrm{V} and R_L = 2\mathrm{k}\Omega. If a 100\mathrm{k}\Omega resistor is connected between the collector and the base of the transistor, calculate the quiescent collector current. Assume V_{BE} = 0.

An X-ray beam of wavelength \lambda_1 undergoes a first order Bragg reflection at a Bragg angle of 30^\circ. X-ray of wavelength 97\,\mathrm{nm} undergoes 3rd order reflection at a Bragg angle of 60^\circ. Consider that the two beams are reflected from the same set of planes. Find the value of \lambda_1.

Calculate the pinch-off voltage for n-channel silicon FET with a channel width of 6 \times 10^{-4}\ \mathrm{cm} and a donor concentration of 10^{15}\ \mathrm{cm}^{-3}. Given that dielectric constant of silicon is 12.

Sketch the dc load line for the circuit shown.

What are the properties of the particles made up of the following quarks?

(i) u\bar{d}

(ii) \bar{u}d

(iii) dds

(iv) uss

Show that in the nuclear shell model, the level spacing between major oscillator shells is approximately \hbar\omega=41A^{-1/3}\,\mathrm{MeV}.

\rho^{0} and K^{0} mesons both decay mostly to \pi^{+} and \pi^{-}. Explain why the mean lifetime of \rho^{0} is shorter (\sim 10^{-23}\,\mathrm{s}) compared to the mean lifetime of K^{0} (\sim 10^{-10}\,\mathrm{s}).

What are chain reactions? What do you mean by critical size of the core in which chain reaction takes place?