question_answer

Find the force needed to hold the wedge in equilibrium, if there is no friction

A) \[\frac{mg}{\cos \theta }\]                  

B) \[mg\,\sin \theta \]        

C)    \[mg{{\sin }^{2}}\theta \]   

D)   \[mg\cos \theta \sin \theta \] 

Correct Answer: D

Solution :

For the block, \[N=mg\cos \theta \] For the horizontal equilibrium of the wedge, \[F=N\sin \theta \] \[\therefore \]\[F=mg\cos \theta \sin \theta \] Hence, the correction option is (d).