A sphere of mass 20 kg is suspended by a metal wire of u stretched length 4 m and diameter 1 mm. When in equilibrium, there is a clear gap of 2 mm between the sphere and the floor. The sphere is gently pushed abide so that the wire makes an angle θ with the vertical and is released. Find the maximum value of θ so that the sphere does not rub the floor. Young modulus of the metal of the wire is 2.0 × 1011 N m-2. Make appropriate approximations.
36.4o
Given, mass of sphere, 
Length of metal wire, 
Young modulus of the wire, 
As the sphere shouldn’t touch the floor, the maximum elongation in the wire is 
.
At the lowest point (Equilibrium), the tension in the wire is 
At the point of release, the tension is 
Now, any change in elongation is due to the change in tension. This change in tension comes from the centrifugal force.
Therefore the force which brings elongation is centrifugal force, 
—————(1)
Where r is the length with elongation.
From work energy theorem,
—————(2)
Substituting (2) in (1)
We know, stress, 
And strain is given by , 
Young’s modulus then becomes, 
