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With what minimum speed v must a small ball be pushed inside a smooth vertical tube from a height h so that it may reach the top of the tube?
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Important Questions on Circular Motion

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A smooth sphere of radius R is made to in a straight line with constant acceleration g. A particle kept on top of the sphere is released from there with zero velocity w.r.t. sphere. The speed of particle
w.r.t sphere as a function of θ is,
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Tangential acceleration of a particle moving on a circle of radius 1 m varies with time t as shown in the graph (initial velocity of the particle is zero). Time after which total acceleration of particle makes an angle of 30° with radial acceleration is
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A bob attached to a string is held horizontal and released. The tension T and vertical distance h from point of suspension can be represented by 

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EASY
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A ball enters a semicircular tube with velocity v and maintains a constant velocity. Find the average force required to keep the tube stable.
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Consider an object of mass m that moves in a circular orbit with constant velocity v0 along the inside of a cone. Assume the wall of the cone to be frictionless. Find the radius of the orbit.
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A bullet is moving horizontally with certain velocity. It pierces two paper discs rotating coaxially with angular speed ω separated by a distance l. If the hole made by bullet on second disc is shifted by an angle θ with respect to the first, find velocity of bullet.
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Given is the α-t graph for a car wheel, where brakes produce an angular acceleration α. Which of the following can be the form of θ-t graph?

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A cyclist is going on an overbridge with constant speed. The value of frictional force acting on the cycle
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