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 = $\frac{q}{2}.$

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

$F_{Net}=\left|F_1-F_2\right|$

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

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

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

= $\frac{9-6}{4}F=\frac{3}{4}F$

<p>For sphere ‘C’ after contacting with ‘A’. q_A = q_C =&nbsp;<math><mrow><mfrac><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>.</mo></mrow></math></p><p>offer contacting with ‘B’. q_B = q_C =&nbsp;<math><mrow><mfrac><mrow><mn>3</mn><mi>q</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></math></p><p><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></p><p>F₂ =&nbsp;<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></p><p><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></p><p><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></p><p>=&nbsp;<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></p><div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1753869364phpvwI0Lt.jpeg" alt="" width="169" height="166" loading="lazy"></picture></div></div>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment