Question

A block of mass $m$ slides in an inclined right angle trough as shown in the figure-2.177. If the coefficient of kinetic friction between the block and the material composing the trough is $\mu$, then the acceleration of the block will be :

• A. $(\cos \theta-\mu \sin \theta) g$
• B. $(\sin \theta-\mu \sin \theta) g$
• C. $(\sin \theta-\mu \cos \theta) g$
• D. $(\sin \theta-\sqrt{2} \mu \cos \theta) g$

Answer 1

Answer: (D)

Friction force acting on block

$ \sqrt{2} N =m g \cos \theta $
$ F_{r} =2 \mu N $
$=2 \mu\left(\frac{m g \cos \theta}{\sqrt{2}}\right) $
$=\sqrt{2} \mu m g \cos \theta $
$a =\frac{m g \sin \theta-\sqrt{2} \mu m g \cos \theta}{m} $
$ \Rightarrow a =(\sin \theta-\sqrt{2} \mu \cos \theta) g $