UPSC Physics Optional PYQs (CSE & IFoS)PYQs

A vessel of mass 10^7\text{ kg} is gyrostabilised by a uniform circular disc of mass 5\times 10^4\text{ kg} and radius 2\text{m} which rotates at 15\text{ rev/sec}. What is the angular momentum of the stabilizer ?

What is the recoil energy in electron-volts of a nucleus of mass 10^{-23}\text{ gm} after emission of x-ray of energy 1\text{ MeV}?

Show from the Lorentz transformation that two events (t_1=t_2) at different points (x_1 \neq x_2) in reference frame S are not in general simultaneous in reference frame S which is moving in the + direction with the constant velocity V with respect to S.

What is the momentum of a proton having kinetic energy 1\text{ BeV} ? The energy equivalent to proton rest mass is 0.938\text{ BeV}.

Water is flowing through a horizontal pipe line of varying cross-section. If the pressure of water equals 2\text{cm} of mercury at a point where velocity of the flow is 32\text{ cm/sec}. What is the pressure at another point where velocity of flow is 40\text{ cm/sec}?

Two objects (M_1=2\text{ gm}: M_2=5\text{ gm}) process Velocities V_1= 10\hat{x}\text{ cm/sec}, V_2 = 3\hat{x}+ 5\hat{y}\text{ cm/sec} just prior to a collision during which they become permanently attached to each other. What is the final momentum of combination of the laboratory system ?

Write a short note on Motion of rocket under constant force field.

What is the angular momentum (referred to the centre of the orbit) of a satellite of mass M, which moves round the earth in a circular orbit of radius r? The result is to be expressed in terms only r, G.M, and M_e (the mass of the earth).

Find the expression for the rise of a liquid between two parallel plates separated by a distance t and dipped vertically in the liquid.

A steel ball 1.00\text{ mm} in diameter falls at a constant speed of 0.176\text{ cm s}^{-1} in a large vessel filled with oil. Calculate the dynamic viscosity of the oil (Density of steel = 7,700\text{ kg/m}^3 density of oil = 900\text{ kg/m}^3).

Write a note on Predictions of general theory of relativity and their experimental verification.

Show that the kinetic energy T of relativistic particle moving with momentum p is T = P^2 / m + m_0 What m_0 its rest mass and m is its relativistic mass.

A muon (\mu meson) is for med high up in the atmosphere and travels towards the earth with a speed of 0.992\text{ c}. It decays af ter travelling a distance of 6.0\text{ km}. In what time does the muon decay as measured (i) by us and (ii) in its own frame of reference? What is the distance covered the muon in its own frame of reference?

For an isotropic solid define Young's modulus of elasticity Y, coefficient of rigidity \eta and Poisson's ratio \alpha. Establish the relation. \sigma = \frac{Y - 2\eta}{2\eta}

The mean distance of the Earth from the Sun is 1.496 \times 10^{11}\text{ m}, while that of Saturn is 1.427 \times 10^{12}\text{ m}. Find the time taken by Saturn to complete one revolution round the Sun.

Find the linear acceleration of the center of gravity of a uniform disc which rolls down an inclined plane without slipping. The angle of inclination is 30^\circ.

Air is blown through a pipe AB, at a rate of 15\text{ litres per minute}. The area of cross-section at A is 2\text{ cm}^2 whereas at B it is 0.2\text{ cm}^2. A tube abc, containing some water, is connected as shown. Find the difference in height, \Delta h, between the levels of water in the tube abc.

Write a note on Coriolis force and its manifestations.

Water is observed to flow through a capillary of diameter 1.0\text{ mm} with a speed of 3\text{ ms}^{-1} viscosity of water in c.g.s. units is : 0.018 at 0^{\circ}\text{C} 0.008 at 30^{\circ}\text{C} 0.004 at 70^{\circ}\text{C} Calculate he Reynolds numbers, and test at which of these three temperatures is the flow likely to be streamlined.

The earth receives from the Sun 1.37\times 10^{3}\text{ W/m}^{2} of power on the top of the atmosphere. Calculate the mass of the Sun that is converted into energy in one second.