Question

An object of mass $m$ is tied to a string of length $L$ and a variable horizontal force is applied to it which starts at zero and gradually increases until the string makes an angle $\theta$ with the vertical. Work done by the force $F$ is:

• A. $mgL(1-\sin \theta )$
• B. $mgL$
• C. $mgL(1-\cos \theta )$
• D. $mgL(1+\cos \theta )$

Answer 1

The correct option is C $mgL(1-\cos \theta )$

Applying work energy theorem on object from $A\to B$

$w_{all}=\Delta K$

$\Rightarrow w_{all}=0$

$\Rightarrow w_f+w_g=0$

$\Rightarrow w_f=-w_g$

$=-(-mgh)$

$\Rightarrow w_f=mgh$

$\Rightarrow w=mg(L-L\cos \theta )$

$\Rightarrow w=mgL(1-\cos \theta )$