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Q.

Four forces of magnitudes P, 2P, 3P and 4P act along the four sides of a square ABCD in cyclic order. If the magnitude of their resultant is $n \sqrt{2} P$ find the value of n.

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answer is 2.

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Detailed Solution

Drawing the four vectors from a common point 'O' in xy plane

Question Image

$θ = 180 + 45; θ = 225$

$θ = (15)^{2}; n = 2$

$∴ \vec{OL} + \vec{OM} + \vec{ON} + \vec{OQ} = \vec{R}$

$\Rightarrow \vec{R} = - 2 Pi - 2 P \hat{j} \Rightarrow | \vec{R} | = 2 P \sqrt{2} ∴ n = 2$

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Four forces of magnitudes P, 2P, 3P and 4P act along the four sides of a square ABCD in cyclic order. If the magnitude of their resultant is n2P find the value of n.