Two identical weightless rods are hinged to each other and to a horizontal beam (Fig.). The rigidity of each rod is `k_(0)`, and the angle between them is `2alpha`. Determine the rigidity k of the system of rods relative to the vertical displacement of a hinge A under the action of a certain force F, assuming that displacements are small in comparison with the length of the rods.

Two rods A and B of same length and cross-sectional area are connected in series and a temperature difference of 100^@C is maintained across the combination as shoen in Fig. If the thermal conductivity of the rod A is 3 k and that of rod B is k, Then i.Determine the thermal resistance of each rod. ii. determine the heat current flowing through each rod. iii. determine the heat current flowing through each rod. iv. plot the variation of temperature along the length of the rod.

A weightless rigid rod AB of length / connects two equal masses m one particle is fixed at the end B and the other at the middle ofthe rod as shown in the figure-5.131. The rod can rotate in the vertical plane freely around the hinge point/4. Choose the correct option(s)

Two rods of the same proper length l_0 move toward each other parallel to a common horizontal axis. In the reference frame fixed to one of the rods the time interval between the moments, when the right and left ends of the rods coincide, is equal to Deltat . What is the velocity of one rod relative to the other?

Three weightless rods of length 1 each are hinged at points A and B lying on the same horizontal and joint through hinges at points C and D (Fig. ). The length AB = 2l . A load of mass m is suspended at the hinge C. Determine the minimum force F_(min) aplied to the hinge D for which the middle rod remains horizontal.

A system of two identical rods (L-shaped) of mass m and length l are resting on a peg P as shown in the figure. If the system is displaced in its plane by a small angle theta ,find the period of oscillations:

Two long conducting rods suspended by means of two insulating threads as shown in Fig. are connected at one end to a charged capacitor through a switch S, which initially open. At the other end , they are connected by a loose wire. The capacitor has charge Q and mass per unit length of the rod is lambda . The effective resistance of the circuit after closing the switch is R. Find the velocity of each rod when the capacitor is discharged after closing the switch. (Assume that the displacement of rods during the discharging time is negligible.)

A rod of mass m and length L is kept on a horizontal smooth surface. The rod is hinged at its one end A . There are two springs, perpendicular to the rod, kept in the same horizontal plane. The spring of spring constant k is rigidly attached to the lower end of rod and spring of spring constant 12k just touches the rod at its midpoint C , as shown in the figure. If the rod is slightly displaced leftward and released then, the time period for small osciallation of the rod will be

A weightless rigid rod with a small iron bob at the end is hinged at point A to the wall so that it can rotate in all directions. The rod is kept in the horizontal position by a vertical inextensible string of length 20cm , fixed at its midpoint. The bob is displaced slightly perpenducular to the plane of the rod and string. Find period of small oscillations of the system in the form (piX)/(10)s and fill the value of X.