A solid sphere is rolling on a surface as shown in figure, with a…

MCQ

A solid sphere is rolling on a surface as shown in figure, with a translational velocity $v\,ms^{-1}$. If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is

A
$\sqrt {2gh} $
B
$\sqrt {\frac{7}{5}gh} $
C
$\sqrt {\frac{7}{2}gh} $
✓
$\sqrt {\frac{10}{7}gh} $

✓

Answer

Correct option: D.

$\sqrt {\frac{10}{7}gh} $

d
Minimum velocity for a body rolling without slipping

$v = \sqrt {\frac{{2gh}}{{1 + \frac{{{K^2}}}{{{R^2}}}}}} $

For solid sphere, $\frac{{{K^2}}}{{{R^2}}} = \frac{2}{5}$

$\therefore v = \sqrt {\frac{{2gh}}{{1 + \frac{{{K^2}}}{{{R^2}}}}}} = \sqrt {\frac{{10}}{7}gh} $

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