Question

Two forces with a magnitude $ 10$ units each are acting as shown in the diagram, their resultant magnitude is?

10 dynes 100 120° 40 dynes

• A. $20\mathrm{dynes}$
• B. $10\mathrm{dynes}$
• C. $5\mathrm{dynes}$
• D. $10\sqrt{3}\mathrm{dynes}$

Answer 1

The correct option is B

$10\mathrm{dynes}$

Step 1: Given information

The magnitude of forces is $10$ dynes each.

Step 2: To find

We have to find the resultant magnitude.

Step 3: Calculation

The end result will be a vector. So it has a force tail on top but also ends on the horizontal force's head. The two forces and also the results will undoubtedly construct an equilateral triangle. As a result, the outcome would be a $10$ dyne force operating on a line with a $60°$ downward angle well with horizontal.
The angle formed by two forces applied on opposite sides of a parallelogram is $120°$.

Now,

By using the law of parallelogram, we get

$$\begin{gathered} \mathrm{R}=\sqrt{{\mathrm{A}}^2+{\mathrm{B}}^2+2\times \mathrm{A}\times \mathrm{B}\times \mathrm{Cos\theta }} \\ \mathrm{R}=\sqrt{{10}^2+{10}^2+2\times 10\times 10\times \mathrm{Cos}120°} \end{gathered}$$

We know, $\mathrm{Cos}120°=-\frac{1}{2}$

By substituting the values, we get

$$\begin{gathered} R=\sqrt{{10}^2+{10}^2+2\times 10\times 10\left(-\frac{1}{2}\right)} \\ =\sqrt{100} \\ =10\mathrm{dynes} \end{gathered}$$

Therefore, option B is the correct choice.