Question

A uniform horizontal circular platform of mass 200 kg is rotating at10rpm about a vertical axis passing through its centre. A boy of mass 50 kg is standing at its edge. If the boy moves to the center of the platform , the frequency of rotation would become (a) 7.5 rpm (b)12.5 rpm (c)15 rpm (d)20 rpm

Answer 1

Explanation:

Given A uniform horizontal circular platform of mass 200 kg is rotating at 10 rpm about a vertical axis passing through its centre. A boy of mass 50 kg is standing at its edge. If the boy moves to the center of the platform , the frequency of rotation would become

So here the boy is standing at the edge of a circular platform and moves towards the centre of the platform. So we have moment of inertia. Consider as initial and final.  

So initial moment of inertia will be 50 R^2 + 200 R^2 / 2

                                                           = 150 R^2

Now in the case of final moment of inertia we get

                                                                 200 R^2 / 2 (since it is zero)

                                                            = 100 R^2

So angular momentum conserve about the centre o will be L initial = L final

                                                                                    So Ii ωi = If ω f

                                                                                 150 R^2 x 10 = 100 R^2 ω f

                                                                  So ω f = 15 rpm

So the frequency of rotation would become 15 rpm