## Aptitude Test Problems in PhysicsEdited by S.S. Krotov

Assume that the threads are weightless and inextensible.42.22Aptitude Test Problems in Physics1.38*. 1. Indicate the load which touches the floor first after a certain time t. For the system at rest shown in Fig. assuming that the person continues to slack the rope at the same constant velocity v. A heavy ball of mass m is tied to a weightless thread of length 1. the springs are weightless. A strong horizontal wind is blowing at a constant velocity v.41. Determine the period T of small oscillations. Determine the elongation A/ of the string. assuming that the oscillations of the ball attenuate in a time much longer than the period of oscillations. At the moment when the two loads are at the same height h. determine the accelerations of all the loads immediately after the lower thread keeping the system in equilibrium has been cut. A rubber string of mass m and rigidity k is suspended at one end. The friction of the ball against air is proportional to its velocity relative to the air: Ffr = Itv. and there is no friction at the point of suspension. the upper pulley is released (is able to rotate without friction like the lower pulley). 1.40. A person hoists one of two loads of equal mass at a constant velocity v (Fig. 15).39. 14. the mass of the pulley is negligibly small. The masses of the pulleys and the ropes and the elongation of the ropes should be neglected. 1. A block can slide along an inclined.1.

3. Find the force F of interaction between the capacitors. Determine the strength E of the electric field at the centre of a hemisphere produced by charges uniformly distributed with a density a over the surface of this hemisphere.6. 75this hemisphere by two planes passing through the same diameter and forming an angle cc with each other (Fig. 3. Two parallel-plate capacitors are arranged perpendicular to the common axis. A part of the surface is isolated fromFig. Determine the electric field strength E produced at the same point 0 by the charges located on the isolated surface (on the "mericarp").74Aptitude Test Problems in Physics3. 75). The separation d between the capacitors is much larger than the separation 1 between their plates and than their size.5*. The capacitors are charged to ql and q2 respectively (Fig.4. 76).3. The strength of the electric field produced by charges uniformly distributed over the surface of a hemisphere at its centre 0 is E0. Determine the force F of interaction between two hemispheres of radius R touch-. 3.

## Aptitude Test Problems in Physics

the ball is at point Anof the well edge). riFig. at the moment of maximum ascent.e.4 2A 3 . the segments of the trajectory of the ball inside the well are parabolas (complete para-Fig. ..114Aptitude Test Problems in PhysicsThe magnitude of the vertical velocity component for the first impact against the bottom is 20. 126 bolas are the segments of the trajectory between successive impacts against the bottom). The ball can "get out" of the well if the moment of the maximum ascent along the parabola coincides with the moment of an impact against the wall (i. On this development. and the time of motion from the top to the bottom of the well is t2 = 1/2H/g. 125 Figure 126 shows the vertical plane development of the polyhedron A 1. The time t1is connected to the time t2through the following relation: nti = 2kt2.