A small ball is hung as shown an a string of length L.
(a) If `v_(0) gt sqrt(6 g l)`, find the angle `theta ( lt 90^(@))` [in terms of, `v_(0), g, L`] with the upward vertical at which the string becomes slack.
(b) find the value of `v_(0)` [ in terms of g, L] if the particle passes through point of suspension

A heavy particle is suspended by a stirng of length l. The particle is given a horizontal velocity v_0 . The stirng becomes slack at some angle and the particle proceeds on a parabola.find the value of v_0 if the prticle psses through the ponit of suspension

A mass m is hanging by a string of length l. The velocity v_(0) which must be imparted to it to just reach the top is

Two small balls A and B are interconnected by an inextensible string of legth L. Mass of ball A =m, mass of ball B = m. the balls are resting on a frictionlesss harixontal surgace , with the distance between them =3L.5 In this position ball A is suddenly given a harizontal velocity v_(0) perpendicular to the line joining the two balls. (see fig 4E . 18 (a)) (a) Find the speed of ball B houst after the string becomes taut (b) find the impulse of the tension in string when the string becomes taut. (c) Find the steady tension in string much after the string has become taut.

In example 1.49 find the velocity of the mid point of the rod in terms of its length l, v and theta .

A bob of mass m is suspended by a light string of length L. It is imparted a horizontal velocity v_(0) at the lowest point A such that it completes a semi-circular trajectory in the vertical plane with the string becoming slack on reaching the topmost point C, figure, Obtain an expression for (i) v_(0) (ii) the speeds at points B and C, (ii) the ration of kinetic energies (K_(B)//K_(C)) at B and C. Comment on the nature of the trajectory of the bob after it reahes the poing C.

A particle of mass m suspended by a string of length l revolves in a horizontal circle ( theta is the angle the string makes with vertical). Which of the following statement(s) is // are correct?

A ball attached to a string length L is oscillating line a simple pendulum. Find v in terms of v_0 L alpha and beta .

A small ball of mass m is attached to a string of lengh R and moves in a vertical circle with a speed v m/s about a fixed point O as illustrated in fig. Find the tension in the string, when it makes an angle theta with the vertical, in terms of v, theta and g.