Question

A wooden block of mass $m$ resting on a rough horizontal table is pulled by a force $F$ as shown in figure. If $\mu$ is the coefficient of friction between block and table, its acceleration will

• A. $\frac{\mu F \cos \theta}{m}$
• B. $\frac{\mu F \sin \theta}{m}$
• C. $\frac{F}{m}(\cos \theta+\mu \sin \theta)-\mu g$
• D. $\frac{F}{m}(\cos \theta-\mu \sin \theta)$

Answer 1

Answer: (C)

Forces acting on the block are shown in figure. For vertical direction no motion occurs
$\therefore \quad R+F \sin \theta=m g$
Along horizontal $F \cos \theta-f=m a,$ where $a$ is
acceleration $F \cos \theta-\mu R=m a$
or $ F \cos \theta-\mu(m g-F \sin \theta)=m a$
or $ a=\frac{F}{m}(\cos \theta+\mu \sin \theta)-\mu g$