question_answer

A think rod\[MN\], free to rotate in the vertical plane about the fixed end\[N\], is held horizontal. When the end \[M\] is released the speed of this end, when the rod makes an angle \[\alpha \] with the horizontal, will be proportional to: (see figure)                                                                                           [JEE Online 15-04-2018 (II)]

A)   \[\sqrt{\cos \alpha }\]               

B)   \[\cos \alpha \]

C)   \[\sin \alpha \]  

D)        \[\sqrt{\sin \alpha }\]

Correct Answer: A

Solution :

[a] When the rod makes an angle of

displacement of centre of mass

speed of end

hence  is proportional to