question_answer

Two particles 1 and 2 are allowed to descend on the two friction less chord OH and OB of a vertical circel, at the same instant from point O. The ratio of the velocities of the particles 1 and 2 respectively, when they reach on the circumference will be (OB is the diameter):

A)  \[\sin a\]                     

B)  \[tan\text{ }a\]

C)  \[cos\text{ }a\]             

D)  none of these

Correct Answer: C

Solution :

    Here, \[OA=d\cos \alpha \]  \[\therefore \]    \[80\,A=g\,\cos \alpha \]             \[\Rightarrow \]                \[V_{A}^{2}=2g\cos \,\alpha \,\,d\,\cos \alpha \]             and      \[V_{B}^{2}=2gd\] \[\Rightarrow \]               \[\frac{{{V}_{A}}}{{{V}_{B}}}=\cos \alpha \]