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) The angle made by the string with the upward vertical, when it becomes slack 
(b) the speed of the particle at this instant is 
(c) the maximum height reach by the particle over the point of suspension is 
Given
The length string is given as 15 cm and a horizontal velocity of 
m/s. the acceleration due to gravity is taken as g = 10 m/s2.
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 r is the length of the rod/thread attached with the bob, m is the mass of the bob, 
is the velocity of the bob.
Explanation
(a) The angle made before it becomes slack is given as
Placing the value we get the value of 
as
Using the equation for the bob in terms of centripetal force we get the velocity as
Placing the value of 
in
(b) The speed of the particle present at a particular time is given as
(c) The string becomes slack after losing velocity making the maximum height of
The height is given as 
