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