The sum of two forces P → and Q → is R → such that R → = P → . Find the angle between resultant of 2 P → and Q → and Q → , ________

So angle between 2 P → + Q → and Q → is 90 o Alternate solution P → + Q → = P → P 2 + Q 2 + 2 P Q cos ⁡ θ = P 2 ⇒ Q + 2 P Q cos ⁡ θ = O ⇒ cos ⁡ θ = - Q 2 P tan ⁡ α = 2 P sin ⁡ θ 2 P cos ⁡ θ + Q = ∞ ∵ 2 P cos ⁡ θ + Q = 0 α = 90 o

Physics - Vectors Question with Solution | TestHub

PhysicsVectorsAddition/SubtractionMedium2 minPYQ_2020

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The sum of two forces $\vec{P}$ and $\vec{Q}$ is $\vec{R}$ such that $|\vec{R}| = |\vec{P}|$ . Find the angle between resultant of $2 \vec{P}$ and $\vec{Q}$ and $\vec{Q}$ , ________

Answer:

90.00

Solution:

So angle between $(2 \vec{P} + \vec{Q})$ and $\vec{Q}$ is $90^{o}$

Alternate solution

$|\vec{P} + \vec{Q}| = |\vec{P}|$
$P^{2} + Q^{2} + 2 P Q \cos θ = P^{2}$
$\Rightarrow Q + 2 P Q \cos θ = O$
$\Rightarrow \cos θ = - \frac{Q}{2 P}$

$\tan α = \frac{2 P \sin θ}{2 P \cos θ + Q} = \infty$
$∵ [2 P \cos θ + Q = 0]$
$α = 90^{o}$

Stream:JEESubject:PhysicsTopic:VectorsSubtopic:Addition/Subtraction

⏱ 2mℹ️ Source: PYQ_2020

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