
Two identical cubes and of same mass and side are placed one over the other as shown in figure. is attached to one end of a spring of force constant . The other end of the spring is attached to a wall. The system is resting on a smooth horizontal surface with the spring in the relaxed state. A small object of mass moving horizontally with speed at a height above the horizontal surface hits elastically the block along the line of their centre of mass. There is no friction between and :
(a) find the minimum value of (say ) such that block will topple over block
(b) if find the amplitude of oscillation of block spring system.

Important Questions on Rotational Motion
A long ladder weighing leans on a frictionless wall. Its feet rest on the floor away from the wall as shown in the figure. If and are the reaction forces of the floor and the wall, then ratio of will be :
(Use .)

Shown in the figure is rigid and uniform one meter long rod held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is off mass and has another weight of mass hung at a distance of from . The tension in the string at is:

One end of a horizontal uniform beam of weight and length is hinged on a vertical wall at point and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point , at a height above the hinge at point . A block of weight is attached at the point of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of . Which of the following statement(s) is(are) correct?





A uniform rod of length and mass is balanced on a wedge placed at mark. A mass of is suspended from the rod at and another unknown mass is suspended from the rod at mark as shown in the figure. Find the value of such that the rod is in equilibrium.





A bead of mass stays at point on a wire bent in the shape of a parabola and rotating with angular speed (see figure). The value of is (neglect friction)

A football of radius is kept on a hole of radius made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted making an angle from the horizontal as shown in the figure below. The maximum value of so that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale)


Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force at a point above its centre of mass (see figure). If the coefficient of friction is , the maximum possible value of for a box not to topple before moving is ________



A bullet of mass m moving with a speed

Find the greatest height at which force may be applied to slide the block without tipping over.

A uniform solid sphere of radius is rolling without sliding on a horizontal surface with a velocity . It collides with an obstacle of height inelastically. Find the angular speed of the sphere just after the collision.

Represent the union of two sets by Venn diagram for each of the following.
is a prime number between and
is an odd number between and



