I.E. Irodov Question Number 1.1: A motorboat going downstream overcame a raft at a point A; \tau = 60\rm \ min later it turned back and after some time passed the raft at a distance l = 6.0\rm \ km from the point A. Find the flow velocity assuming the duty of the engine to be constant.

I.E. Irodov Question Number 2.1 : A vessel of volume V = 30\rm \ l contains ideal gas at the temperature 0^0\rm \ C. After a portion of the gas has been let out, the pressure in the vessel decreased by \Delta P = 0.78\rm \ atm (the temperature remaining constant). Find the mass of the released gas. The gas density under the normal conditions \rho = 1.3\rm \ g/l.

I.E. Irodov Question Number 2.2: Two identical vessels are connected by a tube with a valve letting the gas pass from one vessel into the other if the pressure difference \Delta P \geq 1.10\rm \ atm. Initially, there was a vacuum in one vessel while the other contained ideal gas at a temperature T_1 = 27 \rm \ ^0C and pressure P_1 = 1.00\rm \ atm. Then both vessels were heated to a temperature T_2 =1 07\rm \ ^0C. Up to what value will the pressure in the first vessel (which had vacuum initially) increase?

I.E. Irodov Question Number 2.3: A vessel of volume V = 20\rm \ L contains a mixture of hydrogen and helium at a temperature T = 20\rm \ ^0C and pressure P = 2.0\rm \ atm. The mass of the mixture is equal to m = 5.0\rm \ g. Find the ratio of the mass of hydrogen to that of helium in the given mixture.

I.E. Irodov Question Number 2.4: A vessel contains a mixture of nitrogen (m_1 = 7.0\rm \ g) and carbon dioxide (m_2 = 11\rm \  g) at a temperature T = 290\rm \  K and pressure P = 1.0\rm \ atm. Find the density of this mixture, assuming the gases to be ideal.

I.E. Irodov Question Number 3.1: Calculate the ratio of the electrostatic to gravitational interaction forces between two electrons, and between two protons. At what value of the specific charge q/m of a particle would these forces become equal (in their absolute values) in the case of interaction of identical particle?

Rotational Mechanics Question Number 1: A uniform solid sphere of radius r starts rolling down without slipping from the top of another fixed sphere of radius R. Find the angular velocity of the sphere of radius r at the instant when it leaves contact with the surface of the fixed sphere.

Rotational Mechanics Question Number 2: A solid cylindrical pulley with a mass of M = 2\rm \ kg and radius of R = 20\rm \ cm is free to rotate about its axis. A block of mass M = 4\rm \ kg is attached to the pulley with a light string. Assume the string does not stretch or slip. Calculate (a) the tension in the string and (b) the angular acceleration of the pulley.

Oscillations And Waves Question Number 1: A physical pendulum consists of 4\ \rm m long sticks joined together as shown in the figure. What is the pendulum’s period of oscillation about the midpoint of the horizontal stick?

Electric Flux and Gauss Law Question Number 1: A particle of charge q is placed at a corner of a cube of the edge a. What is the flux through (a) each cube face forming that corner and (b) each of the other cube faces?

Electric Flux and Gauss Law Question Number 2: A point charge q of magnitude 4.0\rm\ \mu C is placed at the center of the flat surface of a hemisphere of radius 10 \rm \ cm. What is the electric flux a) through the curved surface of the hemisphere and b) through the flat surface of the hemisphere?

Electric Flux and Gauss Law Question Number 3: A 10\ \rm nc charge is uniformly distributed on a ring of radius 10\ \rm cm. A sphere of radius  10\ \rm cm is constructed with its center on the circumference of the ring as shown in the figure. Find the electric flux through the sphere.