The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance ?

The bob A of a pendulum released from horizontal to the vertical hits another bob B of the same mass at rest on a table as shown in the figure. If the length of the pendulum is 1m, calculate the height to which bob A will rise after collision.

A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev.//min in a horizontal plane. What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N ?

A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 m s^-2 . What is the trajectory of the bob if the string is cut when the bob is:- at its mean position.

A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 m s^-1 . What is the trajectory of the bob if the string is cut when the bob is:- at one of its extreme positions,

Figure shows a conducting rod PQ in contact with metal rails RP and SQ, which are 0.25 m apart in a uniform magnetic field of flux density 0.4T acting perpendicular to the plane of the paper. Ends R and S are connected through a 5 Omega resistance. What is the emf when the rod moves to the right with a velocity of 5ms^(-1) ? What is the magnitude and direction of the current through the 5 Omega resistance? If the rod PQ moves to the left with the same speed, what will be the new current and its direction?

Two fixed, equal, positive charges, each of magnitude 5xx10^-5 coul are located at points A and B separated by a distance of 6m. An equal and opposite charge moves towards them along the line COD, the perpendicular bisector of the line AB. The moving charge, when it reaches the point C at a distance of 4m from O, has a kinetic energy of 4 joules. Calculate the distance of the farthest point D which the negative charge will reach before returning towards C.

Two bodies of masses 1 kg and 3 kg respectively are connected rigidly by a vertical spring. The body of mass 3 kg rests on a smooth horizontal surface. The force constant of the spring is 484Nm^(-1) . From the equilibrium position, the mass of 1 kg is displaced vertically through a distance of 0.02 m and then released. calculate (i) and frequency of oscillation of the mass of 1 kg (ii) the maximum velocity of this mass (iii) its oscillation energy and (iv) the reaction of the table on the mass of 3 kg, when mass 1 kg is having harmonic oscillations.

Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position the two bobs are in contact. One of the bobs is eleased after being displaced by 10^@ so that it collides elastically head-on with the other bob. Draw a graph showing variation in energy of either pendulum with time, for 0le t le 2T , where T is theh period fo each pendulum.