Question

A solid cylinder of mass '$m$' is kept in balance position on a fixed incline of angle $\alpha ={37}^o$ with the help of a thread fastened to its jacket. The cylinder does not slip. What force $F$ is required to keep the cylinder in balance when the thread is held vertically?

• A. $mg/2$
• B. $3mg/4$
• C. $3mg/8$
• D. $5mg/8$

Answer 1

The correct option is C $3mg/8$

Rotational equilibrium : $Fr=fr$ $⟹F=f$ ........(1)

Translational equilibrium : Horizontal direction

$Nsin$ $\alpha =fcos$ $\alpha$ $⟹N=\frac{fcos\alpha }{sin\alpha }$ .......(2)

Vertical direction :

$F+Ncos$ $\alpha +fsin$ $\alpha =mg$

Or $F+\frac{Fco{s}^2\alpha }{sin\alpha }$ $+Fsin$ $\alpha =mg$

Solving we get $F(1+\frac{1}{sin\alpha })=mg$ where $sin\alpha =3/5$

$\therefore$ $F(1+\frac{5}{3})=mg$ $⟹F=\frac{3mg}{8}$