Statement-I : Two forces P → + Q → and P → - Q → where P → ⊥ Q → ,…

1. Statement I is false but Statement II is true.
2. Both Statement I and Statement II are true.
3. Both Statement I and Statement II are false.
4. Statement I is true but Statement II is false.

Solution

${\overrightarrow{F}}_1$ and ${\overrightarrow{F}}_2$ at ${\theta }_1$
$F_{net 1}=\sqrt{P^2+Q^2+P^2+Q^2+2\left(P^2+Q^2\right)\cos {\theta }_1}$
$F_{net 2}=\sqrt{P^2+Q^2+P^2+Q^2+2\left(P^2+Q^2\right)\cos {\theta }_2}$
If $F_{net 1}=\sqrt{3\left(P^2+Q^2\right)}=\sqrt{2\left(P^2+Q^2\right)+2\left(P^2+Q^2\right)\cos {\theta }_1}$
$\Rightarrow \cos {\theta }_1=\frac{P^2+Q^2}{2\left(P^2+Q^2\right)}$
$\Rightarrow {\theta }_1=60°$
$F_{net 2}=\sqrt{2\left(P^2+Q^2\right)}=\sqrt{2\left(P^2+Q^2\right)+2\left(P^2+Q^2\right)\cos {\theta }_2}$
$\Rightarrow \cos {\theta }_2=0 \Rightarrow {\theta }_2=90°$

Asked in: JEE Main 2021 (31 Aug Shift 2)

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