If the resultant of two forces is of magnitud | vedclass

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(A) Let the two forces be $\vec{F_1}$ and $\vec{F_2}$.Given that the magnitude of the resultant $\vec{R} = \vec{F_1} + \vec{F_2}$ is $P$,and the magni

Vedclass · Accepted Answer

$P\sqrt{2}$

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(A) Let the two forces be $\vec{F_1}$ and $\vec{F_2}$.Given that the magnitude of the resultant $\vec{R} = \vec{F_1} + \vec{F_2}$ is $P$,and the magnitude of one force (say $\vec{F_1}$) is also $P$.So,$|\vec{R}| = P$ and $|\vec{F_1}| = P$.Also,the resultant is perpendicular to $\vec{F_1}$,so $\vec{R} \cdot \vec{F_1} = 0$.Since $\vec{R} = \vec{F_1} + \vec{F_2}$,we have $\vec{F_2} = \vec{R} - \vec{F_1}$.Taking the magnitude squared: $|\vec{F_2}|^2 = |\vec{R} - \vec{F_1}|^2 = |\vec{R}|^2 + |\vec{F_1}|^2 - 2(\vec{R} \cdot \vec{F_1})$.Substituting the known values: $|\vec{F_2}|^2 = P^2 + P^2 - 2(0) = 2P^2$.Therefore,$|\vec{F_2}| = \sqrt{2P^2} = P\sqrt{2}$.

If the resultant of two forces is of magnitude $P$ and equal to one of them and perpendicular to it,then the other force is

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