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27 small mercury droplets each of radius R and charge q are combined to form a big drop. The ratio between the potentials of bigger drop to smaller drop is
- a)4
- b)6
- c)9
- d)12
Correct answer is option 'C'. Can you explain this answer?
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27 small mercury droplets each of radius R and charge q are combined ...
Given Data:
- Number of small mercury droplets = 27
- Radius of each small droplet = R
- Charge of each small droplet = q
Formula:
- The potential energy of a droplet is given by the formula: \( U = \frac{3kq^2}{2R} \)
- The potential of a droplet is given by the formula: \( V = \frac{q}{4\pi\epsilon R} \)
Calculation:
1. Potential of a single small droplet:
\( V_{small} = \frac{q}{4\pi\epsilon R} \)
2. Total charge of the bigger drop:
\( Q_{big} = 27q \)
3. Radius of the bigger drop:
\( R_{big} = 3R \)
4. Potential of the bigger drop:
\( V_{big} = \frac{Q_{big}}{4\pi\epsilon R_{big}} = \frac{27q}{4\pi\epsilon(3R)} \)
5. Ratio of potentials:
\( \frac{V_{big}}{V_{small}} = \frac{27q}{4\pi\epsilon(3R)} \times \frac{4\pi\epsilon R}{q} = 9 \)
Therefore, the ratio between the potentials of the bigger drop to the smaller drop is 9, which corresponds to option 'C'.
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27 small mercury droplets each of radius R and charge q are combined to form a big drop. The ratio between the potentials of bigger drop to smaller drop isa)4b)6c)9d)12Correct answer is option 'C'. Can you explain this answer?
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