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

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Correct Answer

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

Step-by-step Solution

Detailed explanation

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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