Question

A small ring B carries a vertical load P and is supported by two strings BA and BC, the latter of which carries at its free end a weight W = 60 N, as shown in figure. The angles that the strings make with the vertical are shown in the figure, What will be the magnitude of load P if the system remains in equilibrium condition?

• A. 80.67 N
• B. 115.91 N
• C. 58.69 N
• D. 131.27 N

Answer 1

The correct option is B 115.91 N

In equilibrium neglecting friction at pulley C, tension in string BC will be same as weight W

$T_{BC}=W=60N$

Now, Under equilibrium

$T_{AB}cos{30}^{\circ }+T_{BC}cos{45}^{\circ }=P$

$T_{AB}sin{30}^{\circ }-T_{BC}sin{45}^{\circ }=0$

$T_{AB}\times \frac{1}{2}=60\times \frac{1}{\sqrt{2}}$

$T_{AB}=60\sqrt{2}N$

Now,

P = $T_{AB}cos{30}^{\circ }+T_{BC}cos{45}^{\circ }$

= $60\sqrt{2}\times \frac{\sqrt{3}}{2}+60\times \frac{1}{\sqrt{2}}=\frac{60(\sqrt{3}+1)}{\sqrt{2}}$

P = 115.91 N