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.
The angle reached before slack is
Given
The horizontal speed of the bob is
Formula Used
The formula for the total energy in terms of kinetic and potential energy is given as
where
The is the total energy in terms of kinetic and potential energy, m is the mass of the object, g is the acceleration in terms of gravity and l is the length of the object.
Explanation
The velocity at the lowest point is given as
The energy generated because of the potential and kinetic energy is calculated as
Replacing the length as
Hence, the angle reached before slack is