question_answer

Two wooden blocks are moving on a smooth horizontal surface such that the mass m remains stationary with respect to block of mass M as shown in the figure. The magnitude of force P is 

A)  \[(M+m)g\,\tan \,\beta \]        

B)  \[g\,\tan \,\beta \]

C)  \[mg\,\cos \,\beta \]                 

D)  \[(M+m)\,g\,\cos ec\,\beta \]

Correct Answer: A

Solution :

 The different forces acting on mass m are shown in the adjoining figure. Acceleration of the system \[=\frac{P}{M+m}\] \[\therefore \] Force on mass, \[m=\frac{Pm}{M+m}\] Let the reaction of m on M be f. Then, \[f=\frac{Pm}{M+m}\] Here, note that a pseudo force will act on the smaller mass m as f in backward to applied force. According to figure, m will be stationary when \[f\,\cos \,\beta \,=\,mg\,\sin \,\beta \] \[\frac{Pm}{M+m}\cos \,\beta =mg\,\sin \,\beta \] \[\therefore \]    \[P(M+m)\,g\,\tan \,\beta \]