Question

What should be the minimum force $P$ to be applied to the string so that block of mass $m$ just begins to move up the frictionless plane.

• A. $M g \tan \theta / 2$
• B. $Mg \cot \theta / 2$
• C. $\frac{ Mg \cos \theta}{1+\sin \theta}$
• D. None

Answer 1

Answer: (A)

Along the plane $P + P \cos \theta= Mg \sin \theta$
$P = Mg \frac{\sin \theta}{(1+\cos \theta)} $
$= Mg \times \frac{2 \sin \frac{\theta}{2} \cos \frac{\theta}{2}}{2 \cos ^{2} \frac{\theta}{2}} $
$P = Mg \tan \frac{\theta}{2}$