First slide

Rolling motion

Question

A solid sphere is rolling on a frictionless surface, shown in figure with a translational velocity vm/s. If it is to climb the inclined surface then v should be

Easy

A

$\geq \sqrt{\frac{10}{7} g h}$
B

$\geq \sqrt{2 g h}$
C

2gh
D

$\frac{10}{7} g h$

Solution

From law of conservation of energy
$\frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2} \geq m g h$
$\frac{1}{2} m v^{2} + \frac{1}{2} (\frac{2}{5} m R^{2}) \frac{v^{2}}{R^{2}} \geq m g h, v \geq \sqrt{\frac{10}{7} g h}$

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