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Balanced and Unbalanced Forces

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Question

In above shown figure, two force X and Y act perpendicular to each other on a body. Calculate the magnitude of the net force on the body.

A

X - Y

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B

X + Y

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C

\sqrt{X - Y}

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D

\sqrt{X^{2} - Y^{2}}

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E

\sqrt{X^{2} + Y^{2}}

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Solution

The correct option is D $\sqrt{X^{2} + Y^{2}}$
Resultant force on the body $F_{R} = \sqrt{X^{2} + Y^{2} + 2 X Y c o s θ}$
As the two forces are perpendicular to each other, thus $θ = 90^{o}$ and $c o s 90^{o} = 0$
$⟹$ $F_{R} = \sqrt{X^{2} + Y^{2}}$

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