Two identical metallic spheres A and B when placed at certain distance in air repel each other with force of F. Another identical uncharged sphere C is first place in contact with A and then in contact with B and finally placed at midpoint between sphere A and B. The force experienced by sphere C will be:

Correct Option - 2


Detailed Solution:

For sphere ‘C’ -> after contacting with ‘A’. q_A = q_C = $\frac{q}{2}.$  

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For sphere ‘C’ -> after contacting with ‘A’. q_A = q_C = $\frac{q}{2}.$  

                                                                                                     offer

contacting with ‘B’. q_B = q_C = $\frac{3q}{4}$  

$F_{Net}=\left|F_1-F_2\right|$  

F₂ =   $\frac{K\cdot 3q^2\times 4}{r^{2}8}=\frac{3}{2}\frac{k{q}^2}{r^2}$

$F_1=\frac{9k{q}^2\times 4}{16r^2}=\frac{9k{q}^2}{4r^2}=\frac{9}{4}F$  

$\therefore F_{Net}=\left|\frac{9}{4}F-\frac{3}{2}F\right|$

=  $\frac{9-6}{4}F=\frac{3}{4}F$  

 

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<p>For sphere ‘C’ -&gt; after contacting with ‘A’. q_A = q_C = <span contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mi>q</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mo>.</mo> </mrow> </math> </span>&lt;!-- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1815224972"> </o:OLEObject>&lt;/xml&gt;&lt;![endif]--&gt;&nbsp;</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; offer</p><p>contacting with ‘B’. q_B = q_C =<span contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>3</mn> <mi>q</mi> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> </mrow> </math> </span> &lt;!-- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1815224973"> </o:OLEObject>&lt;/xml&gt;&lt;![endif]--&gt;&nbsp;</p><p><br><span contenteditable="false"> <math> <mrow> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>N</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo>|</mo> <mrow> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mo>|</mo> </mrow> </mrow> </math> </span>&lt;!-- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1815224974"> </o:OLEObject>&lt;/xml&gt;&lt;![endif]--&gt;&nbsp;</p><p>F₂ = &lt;!-- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1815224975"> </o:OLEObject>&lt;/xml&gt;&lt;![endif]--&gt;&nbsp;<span contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mi>K</mi> <mo>⋅</mo> <mn>3</mn> <msup> <mrow> <mi>q</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>×</mo> <mn>4</mn> </mrow> <mrow> <msup> <mrow> <mi>r</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mn>8</mn> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mfrac> <mrow> <mi>k</mi> <msup> <mrow> <mi>q</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <msup> <mrow> <mi>r</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </math> </span></p><p><br><span contenteditable="false"> <math> <mrow> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>9</mn> <mi>k</mi> <msup> <mrow> <mi>q</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>×</mo> <mn>4</mn> </mrow> <mrow> <mn>1</mn> <mn>6</mn> <msup> <mrow> <mi>r</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>9</mn> <mi>k</mi> <msup> <mrow> <mi>q</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>4</mn> <msup> <mrow> <mi>r</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>9</mn> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> <mi>F</mi> </mrow> </math> </span>&lt;!-- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1815224976"> </o:OLEObject>&lt;/xml&gt;&lt;![endif]--&gt;&nbsp;</p><p><span contenteditable="false"> <math> <mrow> <mo>∴</mo> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>N</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo>|</mo> <mrow> <mfrac> <mrow> <mn>9</mn> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> <mi>F</mi> <mo>−</mo> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mi>F</mi> </mrow> <mo>|</mo> </mrow> </mrow> </math> </span></p><p>=&nbsp;<span contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>9</mn> <mo>−</mo> <mn>6</mn> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> <mi>F</mi> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> <mi>F</mi> </mrow> </math> </span>&lt;!-- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1031" DrawAspect="Content" ObjectID="_1815224978"> </o:OLEObject>&lt;/xml&gt;&lt;![endif]--&gt;&nbsp;</p><div><div><picture><source srcset="" media="(max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1753699593php478q82.jpeg" alt="" width="292" height="263" loading="lazy"></picture></div></div><p>&nbsp;</p>

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