A particle of mass m is allowed to fall freely under gravity on an elastic horizontal surface. The quantum effect become important if the smallest de-Broglie wavelength of the particle is of the same order as the height from which it was dropped. Write the mechanical energy of the particle if quantum effects become important

A particle of mass m is released from rest at point A in the figure falling freely under gravity parallel to the vertical Y -axis. The magnitude of angular momentum of particle about point O when it reaches B is (where OA=b and AB=h )

A particle of mass m is flying horizontally at velocity u. It strikes a smooth inclined surface and its velocity becomes vertical. (a) Find the loss in kinetic energy of the particle due to impact if the inclination of the incline is 60^(@) to the horizontal. (b) Can the particle go vertically up after collision if inclination of the incline is 30^(@) ?

A particle of mass m is projected upwards from the surface of the earth with a velocity equal to half the escape velocity. (R is radius of earth and M is mass of earth)Calculate the potential energy of the particle at its maximum. Write the kinetic energy of the particle when it was at half the maximum height.

A particle of mass 'm' is raised to a height h = R from the surface of earth. Find increase in potential energy. R = radius of earth. g = acceleration due to gravity on the surface of earth.

A nonconducting disk of radius a and uniform positive surface charge density sigma is placed on the ground, with its axis vertical. A particle of mass m and positive charge q is dropped, along the axis of the disk, from a height H with zero initial velocity. The particle has q//m = 4 epsilon_(0) g// sigma . (i) Find the value of H if the particle just reaches the disk. (ii) Sketch the potential energy of the particle as a function of its height and find its equilibrium position.

A rod AB of mass 3m and length 4a is falling freely in a horizontal position and c is a point distance a from A . When the speed of the rod is u , the point c collides with a particle of mass m which is moving vertically upwards with speed u . if the impact between the particle and the rod is perfectely elastic find The angular velocity of the rod immediately after the impact

A particle A of mass 2m is held on a smooth horizontal table and is attached to one end of an inelastic string which runs over a smooth light pulley at the edge of the table. At the other end of the string there hangs another particle B of mass m, the distance from A to the pulley is l. The particle A is then projected towards the pulley with velocity u. (a) Find the time before the string becomes taut, and shown that after the string becomes taut, the initial velocity of A and B is 4u//3 . (b) Find the common velocity when A reaches the pulley (assume that B has not yet reached the ground).