Questions in Motion in A Plane

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If the length of the second's hand in a stop clock is 3 cm the angular velocity and linear velocity of the tip is
In a circus stuntman rides a motorbike in a circular track of radius \[R\] in the vertical plane. The minimum speed at highest point of track will be
A block of mass \[m\] at the end of a string is whirled round in a vertical circle of radius \[R\]. The critical speed of the block at the top of its swing below which the string would slacken before the block reaches the top is
A sphere is suspended by a thread of length \[l\]. What minimum horizontal velocity has to be imparted the ball for it to reach the height of the suspension
A bottle of sodawater is grasped by the neck and swing briskly in a vertical circle. Near which portion of the bottle do the bubbles collect
A bucket tied at the end of a 1.6 m long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill, when the bucket is at the highest position (Take \[g = 10m/{\sec ^2}\])
A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first 2 sec, it rotates through an angle \[{\theta _1}\]. In the next 2 sec, it rotates through an additional angle \[{\theta _2}\]. The ratio of \[\sqrt 3 mg\] is
A 1 kg stone at the end of 1 m long string is whirled in a vertical circle at constant speed of 4 m/sec. The tension in the string is 6 N, when the stone is at ($g = 10 m/sec^2$)
A cane filled with water is revolved in a vertical circle of radius 4 meter and the water just does not fall down. The time period of revolution will be
A 2 kg stone at the end of a string 1 m long is whirled in a vertical circle at a constant speed. The speed of the stone is 4 m/sec. The tension in the string will be 52 N, when the stone is

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