question_answer

A wooden block of mass M resting on a rough horizontal surface is pulled with a force F at an angle with the horizontal. If\[\mu \]is the coefficient of kinetic friction between the block and the surface, then acceleration of the block is

A)  \[\frac{F}{M}(\cos \phi +\mu \sin \phi )-\mu g\]

B)  \[F\sin \frac{\phi }{M}\]

C)  \[\mu F\cos \phi \]

D)  \[\mu Fsin\,\phi \]

Correct Answer: A

Solution :

                 \[R=Mg-F\,\sin \phi \] \[f=\mu R=\mu =(Mg-F\sin \phi )\] \[F=\cos \phi -f=Ma\] \[a=\frac{1}{M}[F\cos \phi -f]\] \[a=\frac{1}{M}[F\cos \phi -\mu (Mg-F\sin \phi )]\] \[=\frac{F}{M}cos\phi -\mu g+\frac{\mu F}{M}\sin \phi \] \[=\frac{F}{M}[\cos \phi +\mu \sin \phi ]-\mu g\]