Question

A block placed on a horizontal surface is being pushed by a farce $F$ making an angle $theta$ with the vertical. The coefficient of friction between block and surface is $\mu$. The force required to slide the block with uniform velocity on the floor is:

• A. $\frac{\mu mg}{(\sin \theta -\mu \cos \theta )}$
• B. $\frac{(\sin \theta -\mu \cos \theta )}{\mu mg}$
• C. $\mu mg$
• D. $Noneofthese$

Answer 1

Answer: (A)

$\frac{\mu mg}{(\sin \theta -\mu \cos \theta )}$

(Refer to Image 1)

$FBD$

(Refer to Image 2)

Net force must be zero for zero acceleration

$F\sin \theta =\mu mg+\mu F\cos \theta$

$\Rightarrow F=\frac{\mu mg}{\sin \theta -\mu \cos \theta }$