A uniform cylinder of mass M and radius R


A uniform cylinder of mass $M$ and radius $R$ is to be pulled over a step of height $a(a

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

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

  3. $\mathrm{Mg} \frac{a}{R}$

  4. $M g \sqrt{1-\frac{a^{2}}{R^{2}}}$

Correct Option: 1


For step up, $F \times R \geq M g \times x$

$x=\sqrt{R^{2}-(R-a)^{2}}$ from figure

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

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