**P. 4134.** There is an iron load of mass 10 kg at the end of one of the arms of a balance and at the end of the other arm there is a wooden load of mass also 10 kg. Which end of the lever will tilt downward? To which arm and what size of iron weight must be hanged onto the scale in order to balance it?

(The density of iron is 7800 kg/m^{3}, the density of wood is 600 kg/m^{3} and the density of air is 1,3 kg/m^{3}.)

(3 points)

**P. 4138.** A disc of radius 25 cm and of uniform density can swing (with a small amplitude) about a horizontal axle which is perpendicular to the plane of the base of the disc.

*a*) What is its period in seconds if the axle is 25 cm from the centre of the disc?

*b*) Where must the axle be placed in order that the period is to be 1 s?

*c*) Where must the axle be placed in order that the period is to be the minimum?

(5 points)

**P. 4140.** The centres of two small metal balls, whose radii are equal, are initially at a distance of *r*. If both balls are given different magnitude and opposite charges, and then they are released, they begin to move towards each other. They touch each other and then they move away from each other again. When the distance between their centres is 4*r*, then the force exerted between them is one-twentieth of the initial force exerted between them. The initial charge of one of the balls was 2^{.}10^{-7} C. Calculate the initial charge of the other ball.

(4 points)

**P. 4142.** An object is at a distance of *d* from a screen. The convex lens, placed between them, forms the sharp image of the object at the screen at two different positions, the distance between these positions is *s*.

*a*) Find the focal length, *f*, of the lens.

*b*) Suppose that *d* is known very precisely. When will the uncertainty in the measurement of *s* cause a greater error in the calculation of *f* if the value of *s* is greater or if it is smaller?

(4 points)