A solid sphere is rolling on a surface as shown in figure, with a translational velocity $v$ $\mathrm{m}…

A solid sphere is rolling on a surface as shown in figure, with a translational velocity $v$ $\mathrm{m} \mathrm{s}^{-1} .$ If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is
  1. $\sqrt{2 g h}$
  2. $\sqrt{\frac{7}{5} g h}$
  3. $\sqrt{\frac{7}{2} g h}$
  4. $\sqrt{\frac{10}{7} g h}$

Solution

Minimum velocity for a body rolling without slipping
$
v=\sqrt{\frac{2 g h}{1+\frac{K^{2}}{R^{2}}}}
$
For solid sphere, $\frac{K^{2}}{R^{2}}=\frac{2}{5}$
$
\therefore \quad v=\sqrt{\frac{2 g h}{1+\frac{K^{2}}{R^{2}}}}=\sqrt{\frac{10}{7} g h}
$

Asked in: JEE Mains - Rotational Motion - Test 4

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