question_answer

Two wooden blocks are moving on a smooth horizontal surface such that the mass \[m\] remains stationary with respect to the 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 :

[a] Acceleration of the system: \[a=\frac{P}{M+m}\]                (i) The FBD of mass m is shown in the figure R sin \[\beta \]= ma                    (ii) R cos \[\beta \] =mg                    (iii) From Eqs. (ii) and (iii), we get a= g tan \[\beta \] Putting the value of a in (i), we get P = (M+m)g tan \[\beta \]