Question

A uniform cylinder of mass $M$ and radius $R$ is to be pulled over a step of height a $(a<R)$ by applying a force $F$ at its centre ${}^{\prime }{O}^{\prime }$ perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of $F$ required is :

• A. $Mg\sqrt{1-\frac{a^2}{R^2}}$
• B. $Mg\sqrt{{\left(\frac{R}{R-a}\right)}^2-1}$
• C. $Mg\frac{a}{R}$
• D. $Mg\sqrt{1-{\left(\frac{R-a}{R}\right)}^2}$

Answer 1

Answer: (D)

$(\tau {)}_P=0$
F.R. $-mgx=0$

$x=\sqrt{R^2-(R-a{)}^2}$
$F=mg\frac{X}{R}$
$F=mg\sqrt{1-{\left(\frac{R-a}{R}\right)}^2}$
$=$ minimum value of force to pull