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A small disc is at rest at the top of a rough inclined plane. It rolls without slipping. At the bottom of the inclined plane there is a rough vertical groove of radius ‘R’. In order to loop the groove, the minimum height of incline required is (Assume pure rolling on the inner cylinderical surface of groove)

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$\frac{13 R}{4}$

$\frac{11 R}{4}$

$\frac{9 R}{4}$

$\frac{15 R}{4}$

answer is C.

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Detailed Solution

At the top $\frac{m v^{2}}{R} = m g$
$m g (h - 2 R) = \frac{3}{4} m v^{2} ∴ h = \frac{11 R}{4}$

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