question_answer

A particle \[P\] is moving in a circle of radius \['a'\] with a uniform speed \[v\]. \[C\] 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             [NCERT 1982]

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,             \[{{\omega }_{C}}=\frac{v}{{{r}_{BC}}}=\frac{v}{r}\]             Ratio \[\frac{{{\omega }_{A}}}{{{\omega }_{C}}}=\frac{v/2r}{v/r}=\frac{1}{2}.\]