There are four forces acting at a point P produced by strings as shown in Fig. , which is at rest. Find the forces F₁ and F₂

 

This is a Long Answer type Questions as classified in NCERT Exemplar

Explanation- on resolving forces into rectangular components in equilibrium forces (F₁+1/ $\sqrt[]{2}$ )N are equal to $\sqrt[]{2}N$  and F₂ is equal to ( $\sqrt[]{2}+1/\sqrt[]{2}$ )N

F₁+1/ $\sqrt[]{2}$ = $\sqrt[]{2}$

F₁= $\sqrt[]{2}-1/\sqrt[]{2}$ = $\frac{2-1}{\sqrt[]{2}}=\frac{1}{\sqrt[]{2}}=0.707N$

F₂= $\sqrt[]{2}+\frac{1}{\sqrt[]{\sqrt[]{2}}}=\frac{2+1}{\sqrt[]{2}}=\frac{3}{\sqrt[]{2}}=2.121N$

<p><span lang="EN-IN">This is a Long Answer type Questions as classified in NCERT Exemplar</span></p><p><strong><span lang="EN-IN">Explanation-&nbsp;</span></strong><span lang="EN-IN">on resolving forces into rectangular components in equilibrium forces (F₁+1/<span class="mathml" contenteditable="false"> <math> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> </math> </span></span><span lang="EN-IN">)N are equal to <span class="mathml" contenteditable="false"> <math> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> <mi>N</mi> </math> </span></span><span lang="EN-IN">&nbsp;and F₂ is equal to (<span class="mathml" contenteditable="false"> <math> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> </math> </span></span><span lang="EN-IN">)N</span></p><p><span lang="EN-IN">F₁+1/<span class="mathml" contenteditable="false"> <math> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> </math> </span></span><span lang="EN-IN"> =<span class="mathml" contenteditable="false"> <math> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> </math> </span></span><span lang="EN-IN">&lt;!- [endif]-&gt;</span>&lt;!- [endif]-&gt;</p><div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1751262911phpm8ZbSv.jpeg" alt="" width="343" height="273" loading="lazy"></picture></div></div><p><span lang="EN-IN">F₁= <span class="mathml" contenteditable="false"> <math> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> </math> </span></span><span lang="EN-IN">= <span class="mathml" contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>2</mn> <mo>-</mo> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>0.707</mn> <mi>N</mi> </math> </span></span><span lang="EN-IN">&lt;!- [endif]-&gt;</span>&lt;!- [endif]-&gt;</p><p><span lang="EN-IN">F₂= <span class="mathml" contenteditable="false"> <math> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> <mo>+</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mroot> <mrow> <mrow> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>2</mn> <mo>+</mo> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow> <mrow> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>2.121</mn> <mi>N</mi> </math> </span></span><span lang="EN-IN">&lt;!- [endif]-&gt;</span>&lt;!- [endif]-&gt;</p>

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