A block of mass 200g is kept stationary on a smooth inclined plane by applying a minimum horizontal force F $=\sqrt[]{x}$ N as shown in figure.

 

 

For equilibrium along the incline plane is given by,

F cos 60° = mg sin 60°

  $F=\frac{0.2\times 10\times \sqrt[]{3}}{2\times 1}\times 2$              

  $=2\sqrt[]{3}N=\sqrt[]{12}N$              

<div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1753955140phpKRIj5k.jpeg" alt="" width="285" height="344" loading="lazy"></picture></div></div><p>&nbsp;</p><p>For equilibrium along the incline plane is given by, </p><p>F cos 60° = mg sin 60°</p><p>&nbsp; <span class="mathml" contenteditable="false"> <math> <mrow> <mi>F</mi> <mo>=</mo> <mfrac> <mrow> <mn>0</mn> <mo>.</mo> <mn>2</mn> <mo>×</mo> <mn>1</mn> <mn>0</mn> <mo>×</mo> <mroot> <mrow> <mn>3</mn> </mrow> <mrow></mrow> </mroot> </mrow> <mrow> <mn>2</mn> <mo>×</mo> <mn>1</mn> </mrow> </mfrac> <mo>×</mo> <mn>2</mn> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1815480605"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;&nbsp;</p><p>&nbsp;<span class="mathml" contenteditable="false"> <math> <mrow> <mo>=</mo> <mn>2</mn> <mroot> <mrow> <mn>3</mn> </mrow> <mrow></mrow> </mroot> <mi>N</mi> <mo>=</mo> <mroot> <mrow> <mn>1</mn> <mn>2</mn> </mrow> <mrow></mrow> </mroot> <mi>N</mi> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1815480606"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;&nbsp;</p>

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