Question

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

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

Answer 1

The correct option is B $\frac{F}{M}(cos\varphi +\mu sin\varphi )-\mu g$

$Fcos\varphi -f=maN=Mg-Fsin\varphi Fcos\varphi -\mu (mg-Fsin\varphi )=MaFcos\varphi -\mu Mg+\mu Fsin\varphi =Maa=\frac{F}{M}(cos\varphi +\mu sin\varphi )-\mu g$