Rotational Motion

JEE Main level, single correct, medium

276 of 280

Question 276 of 280

A solid sphere is rolling on a surface as shown in figure, with a translational velocity v m s−1v \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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Answer: (D) 107gh\sqrt{\frac{10}{7} g h}

Minimum velocity for a body rolling without slipping
v=2gh1+K2R2v=\sqrt{\frac{2 g h}{1+\frac{K^2}{R^2}}}
For solid sphere, K2R2=25\frac{K^2}{R^2}=\frac{2}{5}
∴v=2gh1+K2R2=107gh\therefore \quad v=\sqrt{\frac{2 g h}{1+\frac{K^2}{R^2}}}=\sqrt{\frac{10}{7} g h}

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