A uniform cylinder of mass M and radius R is to be pulled over a … - Vidyadip

MCQ

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 $'O'$ 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
$Mg \frac{ a }{ R }$
✓
$M g \sqrt{1-\left(\frac{R-a}{R}\right)^{2}}$

✓

Answer

Correct option: D.

$M g \sqrt{1-\left(\frac{R-a}{R}\right)^{2}}$

d
To Step up,

$F \times R \geq M g \times X$

$\Rightarrow F_{\min }=\frac{M g}{R} \times \sqrt{R^{2}-(R-a)^{2}}$

$\quad\quad\quad\,=M g \sqrt{1-\left(\frac{R-a}{R}\right)^{2}}$

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