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
$\therefore R+F\sin \theta =mg$
Along horizontal $F\cos \theta -f=ma,$ where $a$ is
acceleration $F\cos \theta -\mu R=ma$
or $F\cos \theta -\mu (mg-F\sin \theta )=ma$
or $a=\frac{F}{m}(\cos \theta +\mu \sin \theta )-\mu g$