PYQ Bank

What is understood by the term ‘Coriolis force’? Obtain expressions for velocity and acceleration of a particle in rotating coordinate systems.

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).

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}.

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.

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 ?

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.

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

Write a note on Coriolis force and its manifestations.

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}

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 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).

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.

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

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.

The orbit of the earth is an ellipse wite eccentricity 0.0167. Determine the ratio of the maximum speed of the earth to its minimum speed.

A solid sphere of mass 6\text{ kg}, diameter 20\text{ cm}, and uniform density rolls over a surface with a speed of 2\text{ ms}^{-1}. Calculate its kinetic energy.