UPSC Physics Optional PYQs (CSE & IFoS)PYQs

If the forces acting on a particle are conservative, show that the total energy of the particle which is the sum of the kinetic and potential energies is conserved.

Prove that as a result of an elastic collision of two particles under non-relativistic regime with equal masses, the scattering angle will be 90^\circ. Illustrate your answer with a vector diagram.

A particle describes a circular orbit under the influence of an attractive central force directed towards a point on the circle. Show that the force varies as the inverse fifth power of distance.

Suppose that an S'-frame is rotating with respect to a fixed frame having the same origin. Assume that the angular velocity \vec{\omega} of the S'-frame is given by \vec{\omega}=2t\hat{\imath}-t^{2}\hat{\jmath}+(2t+4)\hat{k} where t is time and the position vector \vec{r} of a typical particle at time t as assumed in S'-frame is given by \vec{r}=(t^{2}+1)\hat{\imath}-6t\hat{\jmath}+4t^{3}\hat{k}. Calculate the Coriolis acceleration at t=1 second.

Calculate the horizontal component of the Coriolis force acting on a body of mass 0.1\ \mathrm{kg} moving northward with a horizontal velocity of 100\ \mathrm{ms^{-1}} at 30^{\circ}\mathrm{N} latitude on the Earth.

Construct an operational amplifier based analog computer to solve the differential equation \frac{d^2v}{dt^2}-\frac{dv}{dt}+2v=0.

Explain the race problem encountered in an RS latch and how it can be avoided. Build a Mod-10 counter using JK flip-flops and explain its working.

What are the rules followed in biasing a bipolar junction transistor when it is used as an amplifier? Show how n-p-n and p-n-p transistors to be used as an amplifier are biased and the direction of flow of base, collector and emitter currents.

Classify diamagnetic, paramagnetic and ferromagnetic materials in terms of their magnetic susceptibility \psi. Plot and explain the variation of \frac{1}{\psi} with temperature for the three materials.

Explain the variation of Magnetisation of Type I and Type II superconductors as a function of applied magnetic field.

Starting from an expression for the group velocity, arrive at an expression for the effective mass of an electron in a semiconductor. Explain the significance of sign of the effective mass.

Metallic iron undergoes a structural phase transition from bcc to fcc at 910^\circ\mathrm{C}. At this temperature, the atomic radii of iron atoms in the bcc and fcc structures are 0.126 \times 10^{-9}\,\mathrm{m} and 0.129 \times 10^{-9}\,\mathrm{m} respectively. Calculate the volume change in percentage during this structural change.

Calculate the recoil energy of {}^{57}_{26}\mathrm{Fe} nucleus when it emits a gamma photon of energy 14\,\mathrm{keV}.

Write down the Bethe-Weizsäcker semiempirical mass formula for a nucleus. Explain the significance of each term occurring in it. Discuss the stability of a nucleus against \beta-decay. What is the effect of pairing term on stability?

What are mirror nuclei? How does the charge independence of nuclear force emerges from this concept?

Determine from the given data whether the following reactions are exothermic or endothermic:

(i) {}^{1}_{1}\mathrm{H}+{}^{3}_{1}\mathrm{H}\rightarrow{}^{2}_{1}\mathrm{H}+{}^{2}_{1}\mathrm{H}

(ii) {}^{12}_{6}\mathrm{C}+{}^{12}_{6}\mathrm{C}\rightarrow{}^{20}_{10}\mathrm{Ne}+{}^{4}_{2}\mathrm{He}

Which of the following reactions are permitted or forbidden by various conservation laws?

(i) k^{\mp}p \longrightarrow \Lambda^0 + \pi^0

(ii) k^+ + n \longrightarrow \Sigma^+ + \pi^0

(iii) \pi^{\mp}p \longrightarrow k^{\mp}\Sigma^+

(iv) \pi^+ + n \longrightarrow k^+ + \Lambda^0

(v) \pi^{\mp}p \longrightarrow \Lambda^0 + k^0

(vi) \pi^{\mp}p \longrightarrow k^+ + \Sigma^-

Why should rotational Raman spectrum show a separation of the first Raman line from the exciting line equal to 6B\ \mathrm{cm}^{-1}, while the separation between successive lines equals to 4B\ \mathrm{cm}^{-1}, where B is the rotational constant?

Describe the vibration-rotation spectra of a polyatomic linear molecule. What are P, Q and R branches? Draw rotational energy levels of the vibrational states v=0 and v=1 and perpendicular vibrational-rotational transitions of a linear polyatomic molecule.

Sodium doublets are produced by transitions 3{}^2p_{1/2}\rightarrow 3{}^2s_{1/2}(D_1) and 3{}^2p_{3/2}\rightarrow 3{}^2s_{1/2}(D_2). Calculate the Landé g-factors for these levels.