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Balanced and Unbalanced Forces

If two forces...

Question

If two forces of $5 N$ each are acting along X and Y axes, then the magnitude and direction of resultant is:

A

5 \sqrt{2}, \frac{π}{3}

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B

5 \sqrt{2}, \frac{π}{4}

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C

- 5 \sqrt{2}, \frac{π}{3}

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D

- 5 \sqrt{2}, \frac{π}{4}

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Solution

The correct option is B $5 \sqrt{2}, \frac{π}{4}$
$- \to F_{1} = 5 ˆ x$
$- \to F_{2} = 5 ˆ y$
The resultant vector then is
$- \to F_{R} = - \to F_{1} + - \to F_{2} = 5 ˆ x + 5 ˆ y$
therefore $,$
$F_{R} = 5 \sqrt{2} N$ and its direction is $45^{0}$ with respect to the $x = a x i s .$
Hence,
option $(B)$ is correct answer.

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