Laws of Motion ...

A stone of mass 1 kg is tied to the end of a string of $$1m$$ length. It is whired in a vertical circel. If the velocity of the stone at the top be $$4m/s$$. What is the tension in the string (at that instant)?

A stone of mass $$1kg$$ is tied to one end of a string of length $$0.5\ m$$. It is whirled in a veretical circular. If the maximum tension in the string is $$58.8N$$, the velocity at the top is

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 s, what is the magnitude & direction of acceleration of the stone: 

Mass $$2m$$ is kept on a smooth circular track of mass $$m$$ , which is kept on a smooth horizontal surface. The circular track is given a horizontal velocity $$\sqrt{2gR}$$ towards left and released. The maximum height reached by $$2m$$ will be ?

A stone is tied to a rope is rotated in a vertical circle with unifrom speed. if the difference between maximum and minimum tension in the rope is $$20N$$, mass of the stone in $$Kg$$ is $$(g=10m/s^{2})$$

A ball of mass m strikes the fixed inclined plane inclined plane after falling through a height h. If it rebounds elastically, the impulse on the ball is:

Two balls of the same mass are dropped from the same height h, on to the floor. The first ball bounces to a height $$h/4$$, after the collision & the second ball to a height $$h/16$$. The impulse applied by the first & second ball on the floor are $$I_1$$ and $$I_2$$ respectively. Then

A system of two blocks $$A$$ and $$B$$ are connected by an inextensible massless strings as shown. The pulley is massless and frictionless. Initially the system is at rest when, a bullet of mass $$m$$ moving with a velocity $$u$$ as shown hits the block $$B$$ and gets embedded into it.  The impulse imparted by tension force to the block of mass $$3m$$ is:

Select the incorrect option:-
($$\tau = torque, \,v = velocity, \,\omega = angular \,velocity, \, a_c = centripetal \, acceleration$$)

A road is banked at an angle of $$30^{o}$$ to the horizontal for negotiating a circular road of radius $$10 m$$. At what velocity a car will experience no friction while negotiating the curve?