question_answer

A trolley is falling on a frictionless inclined plane as shown in figure. The angle of string of pendulum with the ceiling of trolley is \[(\alpha )\] equal to

A) \[{{0}^{o}}\]                                   

B) \[{{90}^{o}}-{{\theta }^{o}}\]

C) \[{{90}^{o}}\]                                 

D) \[{{0}^{o}}\]   

Correct Answer: C

Solution :

Making observations from the frame of the trolley, the situation appears as shown in figure, invoking conditions of equilibrium on the bob along \[x-\]axis yields \[T\cos \alpha +mg\sin \theta =ma\] \[T\cos \alpha =ma-mg\sin \theta \] \[T\cos \alpha =mg\sin \theta -mg\sin \theta \]\[[\because \,a=g\sin \theta ]\] \[\therefore \]\[T\cos \alpha =0\Rightarrow \alpha =\frac{\pi }{2}={{90}^{o}}\] Hence, the correction option is [c].