question_answer 44)

                  A mass of 5 kg is moving along a circular path of radius 1 in. If the mass moves with 300 revolutions per minute, its kinetic energy would be                 (a) \[250\,{{\pi }^{2}}\]              (b) \[100\,{{\pi }^{2}}\]                 (c) \[5\,{{\pi }^{2}}\]                             (d) 0                

Answer:

                  (a) \[K.E.=\frac{1}{2}\,m{{v}^{2}}=\frac{1}{2}\,m{{\omega }^{2}}\,{{r}^{2}}\]                 \[=\,\frac{1}{2}\,m\,\times 4{{\pi }^{2}}\,{{v}^{2}}\,\,{{r}^{2}}\]                 \[=\,\frac{1}{2}\,\times \,5\,\times 4{{\pi }^{2}}\times 25\times 1=250\,{{\pi }^{2}}J\]