Question

Two forces of magnitude A and \(\frac{A}{2}\) act perpendicular to each other. The magnitude of the resultant force is equal to:

• A. \(\frac{A}{2}\)
• B. \(\frac{\sqrt{5A}}{{2}}\)
• C. \(\frac{3A}{2}\)
• D. \(\frac{5A}{2}\)

Answer 1

The Correct Option is B

Step 1: Analyze the given forces.- Let the two forces be F1 = A and F2 = A/2.- The forces are perpendicular to each other.

Step 2: Calculate the resultant force.

Fr = $\sqrt{F_1^2 + F_2^2} = \sqrt{A^2 + (\frac{A}{2})^2}$

Fr = $\sqrt{A^2 + \frac{A^2}{4}}$

Fr = $\sqrt{\frac{4A^2 + A^2}{4}}$

Fr = $\sqrt{\frac{5A^2}{4}}$

Final Answer: The resultant force is $\frac{\sqrt{5}A}{2}$

Answer 2

We can use the Pythagorean theorem and the formula for the magnitude of the resultant force of two perpendicular forces to solve this problem.
According to the Pythagorean theorem, the square of the hypotenuse (i.e., the magnitude of the resultant force) of a right triangle is equal to the sum of the squares of the other two sides (i.e., the magnitudes of the two perpendicular forces). Therefore, we have:
Resultant force squared = \(A^2 + (\frac{A}{2})^2\)
Resultant force squared = \(\frac{5A^2}{4}\)
Resultant force = \(\sqrt{\frac{5A^2}{4}}\) = \(\sqrt{\frac{5}{2}}A\)
According to the formula for the magnitude of the resultant force of two perpendicular forces, the magnitude of the resultant force is equal to the square root of the sum of the squares of the magnitudes of the two perpendicular forces. Therefore, we have:
Resultant force = (\(\sqrt{A^2 + (\frac{A}{2})^2}\))
Resultant force = \(\sqrt{\frac{5A^2}{4}}\) = \(\sqrt{\frac{5}{2}}A\)
Thus, the magnitude of the resultant force is \(\sqrt{\frac{5}{2}}A\). Therefore, the answer is B. \(\sqrt{\frac{5A}{2}}\).
Answer. B