question_answer

A particle P is moving in a circle of radius ?a? with a uniform speed\[\nu \]. C is the centre of the circle and AB is a diameter. When passing through B the angular velocity of P about A and C are in the ratio

A) \[1\,\,:\,\,1\]                               

B) \[1\,\,:\,\,2\]

C) \[2\,\,:\,\,1\]                   

D) \[4\,\,:\,\,1\]

Correct Answer: B

Solution :

Angular velocity of particle P about point A, \[{{\omega }_{A}}=\frac{v}{{{r}_{AB}}}\,\,=\,\,\frac{v}{2r}\] Angular velocity of particle P about point C,                \[{{\omega }_{C}}\,=\,\frac{v}{{{r}_{BC}}}\,=\,\frac{v}{r}\] Radio \[\frac{{{\omega }_{A}}}{{{\omega }_{C}}}=\frac{v/2r}{v/r}=\frac{1}{2}\]