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PhysicsNLMFBD & EquilibriumHard2 minPYQ_2022

PhysicsHardsingle choice

Four forces are acting at a point $P$ in equilibrium as shown in figure. The ratio of force $F_{1}$ to $F_{2}$ is $1 : x$ where $x =$ _____ .

Answer:

Solution:

Here, $θ = 45 °$
Applying equilibrium conditions,
Taking components along $x$ & $y$
Considering right side positive, $\sum F_{x} = 0$
$F_{1} + 1 \sin 45 ° - 2 \sin 45 ° = 0 F_{1} = 2 \sin 45 ° - 1 \sin 45 °$
$F_{1} = \sqrt{2} - \frac{1}{\sqrt{2}} = \frac{2 - 1}{\sqrt{2}} = \frac{1}{\sqrt{2}}$
Taking upward positive, $\sum F_{y} = 0$
$1 \cos 45 ° + 2 \cos 45 ° - F_{2} = 0 F_{2} = 1 \cos 45 ° + 2 \cos 45 °$
$F_{2} = \sqrt{2} + \frac{1}{\sqrt{2}} = \frac{2 + 1}{\sqrt{2}} = \frac{3}{\sqrt{2}}$
$F_{1} : F_{2} = 1 : 3$
$x = 3$

Stream:JEESubject:PhysicsTopic:NLMSubtopic:FBD & Equilibrium

⏱ 2mℹ️ Source: PYQ_2022

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