The bob of a stationary pendulum is given a sharp hit to impart it a horizontal speed of Find the angle rotated by the string before it becomes slack.

A simple pendulum consists of a 50 cm long string connected to a loo g ball. The ball is pulled aside 60 that the string makes an angle f 37^o with the vertical and is then released. Find the tension in the string when the bob is at its lowest position.

Figure (8-E15) shows a smooth track, a part of which is a circle of radius R. A block of mass m is pushed against a spring of spring constant k fixed at the left end and is then released. Find the initial compression of the spring so that the block presses the track with a force mg when it reaches the point P, where the radius of the track is horizontal.

A heavy particle is suspended by a 15 m long string. It is given a horizontal velocity of m/s. (a) Find the angle made by the string with the upward vertical, when it becomes slack. (b) Find the speed of the particle at this instant. (c) Find the maximum height reach by the particle over the point of suspension. Take g = 10 m/s².

A simple pendulum of length L having a bob of mass m i deflected from its rest position by an angle θ and released (figure 8-E 16). The string hits a peg which is fixed at a distance x below the point of suspension and the bob starts going in a circle centred at the peg.

(a) Assuming that initially the bob has a height less than the peg, show that the maximum height reached by the bob equals its initial height.

(b) If the pendulum is released with θ = 90^o and x = L/2 find the maximum height reached by the bob above its lowest position before the string becomes slack.

(c) Find the minimum value of x/L for which the bob goes in a complete circle about the peg when the pendulum is released from θ = 90°.