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6. system of particles and rotational motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics6. system of particles and rotational motion1 Mark
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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