First slide

Rolling motion

Question

A solid sphere of mass 2 kg rolls up a 30⁰ incline with an initial speed of 10 ms^-1. The maximum height reached by the sphere is (Take, g = 10 ms^-2)

Moderate

A

3.5 m
B

7 m
C

10.5 m
D

14 m

Solution

In case of pure rolling of sphere, $\frac{K_{R}}{K_{T}} = \frac{2}{5}$
Total kinetic energy = 7/5 times the translational kinetic energy. At highest point, whole of the kinetic energy will be converted into potential energy.
$∴ m g h = \frac{7}{5} (\frac{1}{2} m v^{2}) or h = \frac{7 v^{2}}{10 g} = \frac{7 (10)^{2}}{10 \times 10} = 7 m$

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