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

Answer 1

Answer: (A)

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