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 to an angle $\theta$ with the vertical. The work done by the force F is

• A. $mglsin\theta$
• B. $mgl(1-sin\theta )$
• C. $mglcos\theta$
• D. $mgl(1-cos\theta )$

Answer 1

The correct option is D $mgl(1-cos\theta )$

The forces acting on the bob are : mg, F and T
$W_T=0[\because$ T is always perpendicular to ds]
$W_{mg}=-mgh=-mgl(1-cos\theta )$
$K{E}_i=0andK{E}_f=0,$
Since the bob is moved slowly.
According to work energy theorem $W_{Total}=\Delta KE$
$\therefore W_T+W_{mg}+W_F=K{E}_f-K{E}_i=0$
$0-mgl(1-cos\theta )+W_F=0$
$\Rightarrow W_F=mgl(1-cos\theta )$