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 simple pendulum consisting of a mass M attached to a string of length L is released from rest at an angle alpha . A pin is located at a distance l below the pivot point. When the pendulum swings down, the string hits the pin as shown in figure. The maximum angle theta which the string makes with the vertical after hitting the pin is

A simple pendulum consisting of a mass M attached to a string of length L is released from rest at an angle alpha . A pin is located at a distance l below the pivot point. When the pendulum swings down, the string hits the pin as shown in figure. The maximum angle theta which the string makes with the vertical after hitting the pin is

(i) A simple pendulum consist of a small bob of mass m tied to a string of length L. Show that the total energy of oscillation of the pendulum is E~=1/2 mg L theta_(0)^(2) when it is oscillating with a small angular amplitude theta_(0) . Assume the gravitational potential energy to be zero of the lowest position of the bob. (ii) Three identical pendulums A, B and C are suspended from the ceiling of a room. They are swinging in semicircular arcs in vertical planes. The string of pendulum A snaps when it is vertical and it was found that the bob fell on the floor with speed V_1 . The string of B breaks when it makes an angle of 30° to the vertical and the bob hits the floor with speed V_2 . The string of pendulum C was cut when it was horizontal and the bob falls to the floor hitting it with a speed V3. Which is greatest and which is smallest among V_1,V_2 and V_3 ?

A ball A of mass m attached to a string of length L is released when the string is horizontal. It strikes another ball B of mass 2 m suspended to another string of length L at rest as shown. Find the maximum angle made by the string if the collision is completely inelastic.

Consider a simple pendulum having a bob attached to a string that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length (l) , mass of the bob (m) and acceleration due to gravity (g). Derive the expression for its time period using the method of dimensions.

Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length (l), mass of the bob (m) and acceleration due to gravity (g). Derive the expression for its time period using method of dimensions.

Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length (l), mass of the bob (m) and acceleration due to gravity (g). Derive the expression for its time period using method of dimensions.