Question

In the given figure, the load weighs 200N, $\theta ={37}^{\circ }$ and beam has negligible mass. Then, the tension in string and horizontal and vertical forces that pivot exerts on the beam is

• A. $T=1000N,F_H=800N,F_V=0$
• B. $T=\frac{1000}{3},F_H=800N,F_V=0$
• C. $T=1000N,F_H=\frac{800N}{3},F_V=0$
• D. $T=\frac{1000}{3}N,F_H=\frac{800N}{3},F_V=0$

Answer 1

The correct option is D $T=\frac{1000}{3}N,F_H=\frac{800N}{3},F_V=0$

It is based on concept of tension in string which is mass less. Then the tension T has the same magnitude at all points throughout the string. The magnitude of acceleration of any number of mass connected through the string is always same.
Torque about hinge will be zero. So,

$WL=\frac{3TL}{5}$
$\Rightarrow W=\frac{3T}{5}$
$T=\frac{5W}{3}=\frac{1000N}{3}$
Also, $F_V+\frac{3T}{5}=mg\Rightarrow F_V=0$
$F_H=\frac{4T}{5}=\frac{800N}{3}$