Question

An object of mass `m` is tied to a string of length `l` and a variable force F is applied on it which brings the string gradually at angle thit `theta` with the vertical. Find the work done by the force `F`
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Answer 1

In this case, three forces are acting on the object

1. tension (T)
2. weight (mg) and
3. applied force (F)
Using work-energy theorem
`W_("net")=Delta KE`
or `" " W_(T)+W_(mg)+W_(F)=0`..........(i)
as `" " DeltaKE=0`
because`" " K_(i)=K_(f)=0`
Further, `W_(T)=0`, as tension is always perpendicular to displacement.
`W_(mg)=-mgh "or" W_(mg)=-mgl(1-cos theta)`
Substituting these values in Eq.(i), we get
`W_(F)=mgl(1-cos theta)`