Question

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 $

Answer 1

The Correct Option is A

$ 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 $