**G. 583.** 2 litres of water, initially at a temperature of \(\displaystyle 20~{}^\circ\)C, was heated for ten minutes by an immersion heater, rated at 500 W. Due to this heating the temperature of the water increased to \(\displaystyle 45~{}^\circ\)C. What was the efficiency of the heating process?

(3 points)

This problem is for grade 1 - 9 students only.

**P. 4865.** Two cars are undergoing uniform straight line motion along two straight motorways, which are perpendicular to each other, as shown in the *figure.* Initially the vehicles were at a distance of \(\displaystyle x_0=6\) km and \(\displaystyle y_0=3\) km from the cross-roads. The speed of the car moving along the path labelled \(\displaystyle AO\) is \(\displaystyle v_1=36~\)km/h. It takes 9 minutes for the cars to reach the position where they are the closest to each other during their motion.

What is the speed of the car travelling along path \(\displaystyle BO\), and what is the shortest distance between them?

(5 points)

**P. 4866.** Two pendulums of length \(\displaystyle l\) are hanging next to each other, such that the balls at their ends are touching each other as shown in the *figure.* The mass of one of the balls, \(\displaystyle M\), is much greater than that of the other, \(\displaystyle m\).

\(\displaystyle a)\) The pendulum on the left is displaced a bit, such that the elevation of the ball of mass \(\displaystyle M\) is \(\displaystyle h\ll \ell\), and then it is released. After the elastic collision of the balls what maximum height can the ball of mass \(\displaystyle m\) reach?

\(\displaystyle b)\) If both balls are deflected into opposite directions, such that both are raised to a height of \(\displaystyle h\ll \ell\), then what may be the maximum height to which the ball of mass \(\displaystyle m\) goes up after colliding elastically with the other ball?

(4 points)

**P. 4869.** A spring (designed for both compression and extension) of length \(\displaystyle \ell\) is compressed to a length of \(\displaystyle d<\ell/2\) with a force of \(\displaystyle F_1\). Then the spring is halved and the two alike springs are held next to each other and compressed (in parallel) again, to a length of \(\displaystyle d\). What is the magnitude of the force \(\displaystyle F_2\), which is to be exerted?

How many equal pieces should a spring of length \(\displaystyle \ell=10d\) be cut into, in order to maximize the force \(\displaystyle F_n\), which is exerted when all the pieces, held parallel, are compressed to a length of \(\displaystyle d\)? What is the magnitude of this force?

(5 points)

**P. 4871.** A particle of mass \(\displaystyle m\) and of charge \(\displaystyle q\) is shot into uniform magnetic field at a speed of \(\displaystyle v\). The magnetic induction of magnitude \(\displaystyle B\), is perpendicular to the plane of the paper. Before entering into the magnetic field the particle is moving parallel to the (lower) rim of the region of magnetic field at a distance of \(\displaystyle d\) from it, as shown in the figure. When passing through the magnetic field the direction of its motion changes by an angle of \(\displaystyle \varphi=60^\circ\).

\(\displaystyle a)\) What is the sign of the charge if the induction vector points into the paper?

\(\displaystyle b)\) What is the speed of the particle?

(4 points)