The given system is displacement by distance 'A' and released. Both the blocks (each of mass m) move together without relative slipping in the whole process. The magnetic of frictionless force between them at time 't' is

where `omega = sqrt((K)/(2m))`

When distance between two given magnetic poles is halved, force between them becoems k times, where k=

A block P of mass m is placed on a smooth horizontal surface. A block Q of the same mass is placed over the block P and the coefficient of static friction between them is mu . A spring of spring constant K is attached to block Q. The blocks are displaced together to a distance A and released. The upper block oscillates without slipping over the lower block. The maximum frictional force between the block is:

A block P of mass m is placed on a smooth horizontal surface. A block Q of the same mass is placed over the block P and the coefficient of static friction between them is mu . A spring of spring constant K is attached to block Q. The blocks are displaced together to a distance A and released. The upper block oscillates without slipping over the lower block. The maximum frictional force between the block is:

(i) In the shown arrangement, both springs are relaxed. The coefficient of friction between m_(2) " and " m_(1) is mu . There is no friction between m_(1) and the horizontal surface. The blocks are displaced slightly and released. They move together without slipping on each other. (a) If the small displacement of blocks is x then find the magnitude of acceleration of m_(2) . What is time period of oscillations ? (b) Find the ratio (m_(1))/(m_(2)) so that the frictional force on m_(2) acts in the direction of its displacement from the mean position. (ii) Two small blocks of same mass m are connected to two identical springs as shown in fig. Both springs have stiffness K and they are in their natural length when the blocks are at point O. Both the blocks are pushed so that one of the springs get compressed by a distance a and the other by a//2 . Both the blocks are released from this position simultaneously. Find the time period of oscillations of the blocks if - (neglect the dimensions of the blocks) (a) Collisions between them are elastic. (b) Collisions between them are perfectly inelastic.

Two point particles of mass m and 2m are initially separated by a distance 4a. They are then released to become free to move. Find the velocities of both the particles when the distance between them reduces to a.

Two point particles of mass m and 2m are initially separated by a distance 4a. They are then released to become free to move. Find the velocities of both the particles when the distance between them reduces to a.

Four identical blocks each of mass m are linked by threads as shown. If the system moves with constant acceleration under the influence of force F, the tension T_(2) is

A block P of mass m is placed on horizontal frictionless plane. A second block of same mass m is placed on it and is connected to a spring of spring constant k, the two blocks are pulled by distance A. Block Q oscillates without slipping. What is the maximum value of frictional force between the two blocks.