Q7.21     A solid cylinder rolls up an inclined plane of angle of inclination 30^{0} . At the bottom
              of the inclined plane the centre of mass of the cylinder has a speed of 5m/s .

            b) How long will it take to return to the bottom?

Answers (1)

The velocity of cylinder is given by : 

                                                             v\ =\ \left ( \frac{2gh}{1\ +\ \frac{k^2}{r^2}} \right )^ \frac{1}{2}

or                                                          v\ =\ \left ( \frac{2gd\sin \Theta }{1\ +\ \frac{k^2}{r^2}} \right )^ \frac{1}{2}

We know that for cylinder : 

                                                          K^2\ =\ \frac{R^2}{2}

Thus                                                    v\ =\ \left ( \frac{4}{3} gd \sin \Theta \right )^\frac{1}{2}

Required time is : 

                                                            t\ =\ \frac{d}{v}

or                                                              =\ \left ( \frac{11.46}{19.6} \right )^\frac{1}{2}\ =\ 0.764\ s

Hence required time is  0.764(2)  =  1.53  s.

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