Question

A $20\text{kg}$ floodlight in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole, as shown in figure. A cable at an angle of ${30}^{\circ }$ with the beam helps to support the light. The vertical force exerted on the beam by the pole is

• A. $392\text{N},\text{down}$
• B. $196\text{N},\text{up}$
• C. $\text{Zero}$
• D. $196\text{N},\text{down}$

Answer 1

The correct option is C $\text{Zero}$

Since the beam is at rest, we can say that $\sum F_x=0$



$\therefore V+T\sin {30}^{\circ }-196=0$

$\Rightarrow V=196-T\sin {30}^{\circ }$

Substituting the data given in the question,

$H=196-392\sin {30}^{\circ }=0\text{N}$