Question

Consider the situation shown in figure. Both the pulleys and the string are light and all the surfaces are frictionless. Calculate the force exerted by the clamp on the pulley A in the figure.

Answer 1

$Ma-2T=0$ $T+Ma-Mg=0$
$\Rightarrow Ma=2T\Rightarrow T=Ma/2$ $\Rightarrow Ma/2+ma=Mg$ (because $T=Ma/2$)
$\Rightarrow 3Ma=2Mg\Rightarrow a=2g/3$
Let $R^1=$ resultant of tensions = force exerted by the clamp on the pulley $R^1=\sqrt{T^2+T^2}=\sqrt{2T}$

$\therefore R=\sqrt{2}T=\sqrt{2}\frac{Mg}{2}=\frac{\sqrt{2}Mg}{3}$

Again, $\tan \theta =\frac{T}{T}=1\Rightarrow \theta ={45}^o$

So, it is $\frac{\sqrt{2}Mg}{3}$ at an angle of ${45}^o$ with horizontal.