Circular Motion and Its Characteristics

Three identical cars A, B and C are moving at the same speed on three bridges. The car A goes on a place bridge, B on a bridge convex upward and C goes on a bridge concave upward. Let F_A, F_B and F_C be the normal forces exerted by the car on the bridges when they are at the middle of bridges. 

A body of M.I. 2 kg m² rotates with an angular velocity of 20 rad/s. When an external torque of 0.5 N m acts on it in the opposite direction, the number of revolutions it makes before it comes to rest is ____________.

When a particle moves in a circle with a uniform speed

A motorcycle has to move with a constant speed on an over bridge which is in the form of a circular arc of radius R and has a total length L. Suppose the motorcycle starts from the highest point.(a) What can its maximum velocity be for which the contact with the road is not broken at the highest point? (b) If the motorcycle goes at speed 1/√2 times the maximum found in part (a), where will it lose the contact with the road? (c) What maximum uniform speed can it maintain on the bridge if it does not lose contact anywhere on the bridge? 

A rope is wound around a solid cylinder of mass 1 kg and radius 0.4 m. What is the angular acceleration of cylinder, if the rope is pulled with a force of 25 N? (Cylinder is rotating about its own axis.)

A particle of mass 1 kg, tied to a 1.2 m long string is whirled to perform the vertical circular motion, under gravity. The minimum speed of a particle is 5 m/s. Consider the following statements.

P) Maximum speed must be `5sqrt5` m/s.

Q) Difference between maximum and minimum tensions along the string is 60 N.

Select the correct option.

A stone tide to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is `sqrt(x("u"^2 - "gL")`. The value of x is ______.

A stone of mass m tied to a string of length l is rotated in a circle with the other end of the string as the centre. The speed of the stone is v. If the string breaks, the stone will move