**P. 4707.** An object of mass \(\displaystyle m=0.2\) kg and another one of mass \(\displaystyle 4m\) can move frictionlessly along a horizontal surface. The greater mass object is attached to an unstretched spring of spring constant \(\displaystyle D=320\) N/m. (The spring is designed for both compression and tension.) The smaller object collides head-on at a speed of \(\displaystyle v_0=5\) m/s with the stationary heavy object. The collision is totally elastic.

\(\displaystyle a)\) What is the maximum compression of the spring?

\(\displaystyle b)\) What will the maximum speed of the object attached to the spring be, and what is the greatest extension of the spring?

(4 points)

**P. 4710.** Some ice at a temperature of \(\displaystyle 0~{}^\circ\)C is added to 1 kg water at a temperature of \(\displaystyle 2~{}^\circ\)C. The mixture is in a thermally insulated container and the amount of ice is such, that it just melts whilst the final temperature of the water will be \(\displaystyle 0~{}^\circ\)C.

\(\displaystyle a)\) Will the entropy of the system increase or decrease?

\(\displaystyle b)\) Give numerical estimation for the change in the entropy of the system.

(5 points)

**P. 4711.** Six alike simple pendulums are made of electrically insulating threads of negligible mass and of small metal spheres of mass 5 g. The length of each pendulum is 0.5 m. The six pendulums are hung at the same point, and then they are all rotated about a vertical axis through this point. After a long enough time each small sphere revolves along a circular path of radius \(\displaystyle r\) in a horizontal plane.

\(\displaystyle a)\) What is the radius \(\displaystyle r\) of the path, if the period of the motion is 1 s?

\(\displaystyle b)\) What same amount of charge should be added to the spheres in order that they stay at the circumference of the same radius of circle \(\displaystyle r\), without rotation?

(4 points)

**P. 4713.** A small ball of mass \(\displaystyle m\) and of charge \(\displaystyle Q\) is hanging on a piece of thread in uniform vertical magnetic field of magnetic induction \(\displaystyle B\). The ball is given an initial velocity such that it undergoes uniform circular motion in a horizontal plane. At another occasion the ball is started such that it moves in the magnetic field along the same radius of circle in the horizontal, but in the opposite direction as it did in the previous case.

\(\displaystyle a)\) Determine the ratio of the two tensions in the thread in the two cases.

\(\displaystyle b)\) What is the difference between the magnitudes of the angular speeds of the two motions?

(4 points)

**P. 4714.** A satellite orbits about the Earth along an elliptical path. The major axis of the ellipse is \(\displaystyle 2a\) and its minor axis is \(\displaystyle 2b\). Determine the velocity of the satellite

\(\displaystyle a)\) at that point of its path which is the closest to the Earth;

\(\displaystyle b)\) at that point of its path which is the furthest from the Earth;

\(\displaystyle c)\) at a point which is at a distance of \(\displaystyle r\) from the centre of the Earth.

(5 points)