Question

A solid cylinder of mass $m$ is kept in balance on fixed incline of angle $\alpha ={37}^{\circ }$ with the help of a thread fastened to its jacket. The cylinder does not slip.
In what direction should the thread be pulled to minimize the force required to hold the cylinder ? What is the magnitude of this force ?

• A. $\frac{3mg}{10}$ parallel to incline
• B. vertical $\frac{3mg}{8}$
• C. horizontal $\frac{mg}{5}$
• D. None of these

Answer 1

The correct option is B vertical $\frac{3mg}{8}$

At equilibrium condition, moment is zero at O

Take clockwise direction positive.

$F(r+r\sin \alpha )-mg\left(r\sin \alpha \right)=0$

$F=\frac{mg\sin \alpha }{1+\sin \alpha }=\frac{3mg}{8}$

Hence, Force is $\frac{3mg}{8}$ vertically upward.