Question

A mass of $Mkg$ 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 ${30}^{}$ with the initial vertical direction. What is the work done by the applied force?

• A. $Mgl(1-\frac{\sqrt{3}}{2})$
• B. $Mgl(1-\frac{1}{2})$
• C. $Mg\frac{l\sqrt{3}}{2}$
• D. $\frac{Mgl}{4}$

Answer 1

The correct option is A $Mgl(1-\frac{\sqrt{3}}{2})$

REF.Image.

Solution - As the mass is displaced

slowly,

$△KE=0$

$W_{gravity}=-mgl(1-\frac{\sqrt{3}}{2})$

By work Energy,

$W_{Total}=△KE$

$\Rightarrow W_{Force}+W_{gravity}=0$

$\Rightarrow W_{Force}=-W_{gravity}$

$=mgl(1-\frac{\sqrt{3}}{2})$

Option - A is correct.