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JEE Main
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Physics
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Mathematics in Physics

JEE Main · Physics · Mathematics in Physics

Consider an object kept at the centre, in the X Y -plane, on which...

Consider an object kept at the centre, in the XYX Y-plane, on which five coplanar forces act as shown in the figure. The resultant force on the object is Consider an object kept at the centre, in the X Y -plane, on which five coplanar forces act as shown in the figure. The

Options

  1. A6.5 N,330∘6.5 \mathrm{~N}, 330^{{}^{{}^{\circ}}}
  2. B6.5 N,300∘6.5 \mathrm{~N}, 300^{{}^{{}^{\circ}}}
  3. C6.5 N,30∘6.5 \mathrm{~N}, 30^{{}^{{}^{\circ}}}
  4. D5.7 N,331∘5.7 \mathrm{~N}, 331^{{}^{{}^{\circ}}}

Correct answer

A. 6.5 N,330∘6.5 \mathrm{~N}, 330^{{}^{{}^{\circ}}}

Step-by-step solution

Consider an object kept at the centre, in the X Y -plane, on which five coplanar forces act as shown in the figure. The
The total force in XX-direction, ΣFx=15cos⁡60∘+19−11cos⁡30∘−16cos⁡45∘ΣFx=5.66 N\begin{aligned}& \Sigma F_x=15 \cos 60^{{}^{{}^{\circ}}}+19-11 \cos 30^{{}^{{}^{\circ}}}-16 \cos 45^{{}^{{}^{\circ}}} \\ & \Sigma F_x=5.66 \mathrm{~N} \end{aligned}The total force in YY-direction, ΣFy=−22+15sin⁡60∘+16cos⁡45∘−11sin⁡30∘ΣFy=−3⋅196 N\begin{aligned}& \Sigma F_y=-22+15 \sin 60^{{}^{{}^{\circ}}}+16 \cos 45^{{}^{{}^{\circ}}}-11 \sin 30^{{}^{{}^{\circ}}} \\ & \Sigma F_y=-3 \cdot196 \mathrm{~N} \end{aligned}Then, resultant force ⇒\quadR=Fx2+Fy2=(5⋅66)2+(3⋅196)2R=6⋅5 N\begin{aligned} \Rightarrow \quadR & =\sqrt{F_x^2+F_y^2}=\sqrt{(5 \cdot 66)^2+(3 \cdot 196)^2}\\ R & =6 \cdot5 \mathrm{~N} \end{aligned}Direction of resultant,⇒tan⁡θ=Fy/Fx=−3⋅1965⋅66⇒θ=330∘\begin{aligned} \Rightarrow& \tan \theta& =F_y / F_x=\frac{-3 \cdot 196}{5 \cdot 66}\\ \Rightarrow & \theta& =330^{{}^{{}^{\circ}}} \end{aligned}
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