A beam of negligible mass is hinged at support P and has a roller support Q as shown in the figure.

A point load of 1200 N is applied at point R. The magnitude of the reaction force at support Q is __________ N.

The correct answer is 1500.

Step-by-Step Explanation:

1. Identify the Support Reactions and Applied Forces from the Diagram:
Based on the provided figures, we have an L-shaped beam of negligible mass:

• Hinge support at point P: A hinge support can exert both horizontal and vertical reaction forces. Since we will take moments about point P, these reaction forces will not produce any moment about P because their moment arms are zero.
• Roller support at point Q: The roller support is mounted against a vertical wall at Q. A roller support only exerts a reaction force perpendicular to its supporting surface. Therefore, the reaction force at support Q, denoted as $R_Q$, acts horizontally.
• Point load of 1200 N at point R: This vertical force acts downwards. From the dimension lines in the image, the horizontal distance from the hinge P to the line of action of this force is $5\text{m}$.
• Height of roller support Q: The vertical height from the horizontal segment of the beam to the roller support Q is $4\text{m}$.

2. Apply the Equilibrium Condition:
For the beam to remain in static equilibrium, the sum of the moments about any point must be equal to zero. Taking moments about support P ($\Sigma M_P=0$):
- The moment due to the 1200 N downward point load at R acts clockwise and has a moment arm of $5\text{m}$:
$M_{\text{clockwise}}=1200\text{N}\times 5\text{m}=6000\text{N}·\text{m}$
- The moment due to the horizontal reaction force $R_Q$ at support Q acts counter-clockwise and has a vertical moment arm of $4\text{m}$:
$M_{\text{counter-clockwise}}=R_Q\times 4\text{m}$

3. Calculate the Reaction Force:
Setting the sum of the moments about point P to zero:

$\Sigma M_P=0$

$1200\times 5-R_Q\times 4=0$

$6000=4R_Q$

$R_Q=\frac{6000}{4}$

$R_Q=1500\text{N}$

Thus, the magnitude of the reaction force at support Q is 1500 N.