\(25.5\, k\,Vm^{-1}\) જેટલા વિદ્યુતક્ષેત્રમાં \(6\) વધારાના ઇલેક્ટ્રોન ધરાવતા પ્રવાહીના ટીપાને સ્થિર રાખવામા આવે છે.પ્રવાહીની ઘનતા \(1.26\times10^3\, kg\, m^{-3}\) હોય તો ટીપાની ત્રિજ્યા કેટલી હશે?

A \(4.3\times10^{-7}\, m\)
B \(7.8\times10^{-7}\, m\)
C \(0.0078\times10^{-7}\, m\)
D \(3.4\times10^{-7}\, m\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(7.8\times10^{-7}\, m\)

Step-by-step Solution

Detailed explanation

\(\mathrm{F}=\mathrm{qE}=\mathrm{mg}\left(\mathrm{q}=6 \mathrm{e}=6 \times 1.6 \times 10^{-19}\right)\) Density \((\mathrm{d})=\frac{\text { mass }}{\text { volume }}=\frac{\mathrm{m}}{\frac{4}{3} \pi r^{3}}\) or \(r^{3}=\frac{m}{\frac{4}{3} \pi d}\) Putting the value of…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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