Consider the Cavendish setup for measuring the gravitational constant (the so-called torsion balance). A light rod (rocker arm), at the ends of which two identical balls of mass m are fixed, is suspended on a thin and long thread. Two balls of mass M, significantly larger than m, can be brought closer to the balls. The rocker arm is equipped with a mirror that casts a light "bunny" on a remote scale and therefore allows you to measure very small angles of rotation of the rocker arm around the vertical axis. (With a rocker arm length of 10 cm and a mirror distance of 40 m from the scale, the displacement of the "bunny" is 1600 times greater than the displacement of the balls.)
The measurement is carried out as follows. Balls of mass M are placed symmetrically near balls of mass m. In this case, the rocker arm is rotated and the thread is twisted at a certain angle. Then, when the large balls are moved to a new symmetrical position after the torsional vibrations stop, the angle of rotation of the rocker arm is measured. Knowing the elastic properties of the thread, determine the maximum acceleration of light balls.
Calculate the gravitational constant based on the data obtained on the Cavendish installation (torsional scales): the distance between balls of mass m and M is 2r = 10 cm, the mass of heavy balls is M = 7.0 kg, and the maximum acceleration of light balls is a = 2.8⋅10−7 m/s2.