Question

A mass of M kg is suspended by a weightless string of length L. A Horizontal force is applied to displace it slowly until the string makes an angle of 30degrees

with the initial vertical direction. what is the work done by the applied force?

Answer 1

Slowly means That at first it's velocity is 0 and also at last the velocity is 0 , or in other words change in Kinetic Energy is 0
we know from work energy theorem that
work done by all ( that is sum of individual work of gravity and our external force in this case = change in Kinetic Energy

so work done by gravity + work done by force =0. (1)
work done by gravity is -mg*(vertical disp)
now the vertical disp is L-Lcos30
so from eq 1 we get
-mgL(1-cos30)+ Work done by ext force = 0
work done by ext force is = mgL(1-√3/2)
That's the Logic part