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Rolling motion on an incline
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A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle inclination $30^\circ$. The centre of mass of cylinder has speed of 4 m/s. The distance travelled by the cylinder on the incline surface will be: (Take $g=10$ m/s$^2$)For a solid cylinder $\frac{k^2}{R^2}=\frac{1}{2}$. $\frac{1}{2}mv^2\left(1+\frac{k^2}{R^2}\right)=mgh \Rightarrow \frac{1}{2}\times2\times16\times\frac{3}{2}=2\times10\times h \Rightarrow h=1.2$ m. Distance along incline $=\frac{h}{\sin30^\circ}=2.4$ m.