Chapter 11 - Virtual Work - Section 11.3 - Principle of Virtual Work for a System of Connected Rigid Bodies - Problems - Page 595: 15

$F=\frac{M}{2asin\theta}$

We can determine the required force as follows: The virtual displacement is given as $\delta_{xA}=\frac{d(2asin\theta)}{d\theta}=-2asin\theta$ The virtual-work equation is $\delta U=0$ $M+F\delta_{XA}=0$ $\implies M+F(-2asin\theta)=0$ This can be rearranged as: $F=\frac{M}{2asin\theta}$