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A drop of mercury is raised to a potential of 90 volts. This is broken into 27 identical drops. The potential of each droplet is a) 2 volts b) 5 volts c) 10 volts d) 15 volts?
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A drop of mercury is raised to a potential of 90 volts. This is broken...
Solution:
Understanding the concept of Charge and Potential
Before we solve the problem, let's understand some basic concepts.
- Charge: Electric charge is a fundamental property of matter. It is the property of matter that causes it to experience a force when placed in an electromagnetic field.
- Potential: Electric potential is a scalar quantity that describes the potential energy per unit of charge at a given point in space.
Calculating the charge on the original drop of mercury
The potential of the original drop of mercury is given as 90 volts.
Since we know that the potential is the potential energy per unit of charge, we can write:
90 volts = Potential energy/Charge
Since the potential energy of a charged sphere is given by the formula:
Potential energy = (3/5) x (Q^2/R)
Where Q is the charge on the sphere and R is the radius of the sphere.
Therefore, we can write:
90 = (3/5) x (Q^2/R) / Q
Simplifying the above equation, we get:
Q = sqrt((90 x 5 x R)/3)
Calculating the potential of each droplet
Now that we know the charge on the original drop of mercury, we can use the fact that the charge is conserved when the drop is broken into smaller droplets.
Since the original drop was broken into 27 identical drops, each drop will have a charge of:
Q/27
Now, the potential of each droplet can be calculated using the formula:
Potential = (3/5) x (Q^2/R)
Substituting the value of Q/27 and solving for potential, we get:
Potential = (3/5) x ((Q/27)^2/R)
Simplifying the above equation, we get:
Potential = (1/27^2) x (3/5) x (Q^2/R)
Therefore, the potential of each droplet is:
Potential = (1/27^2) x 90 volts
Potential = 0.125 volts
Conclusion
The potential of each droplet is 0.125 volts. Therefore, the correct answer is option (a) 2 volts.
Community Answer
A drop of mercury is raised to a potential of 90 volts. This is broken...
10V.V=n^2/3 v.90=27^2/3 v.90=3^2 v.90=9 v.10=v
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A drop of mercury is raised to a potential of 90 volts. This is broken into 27 identical drops. The potential of each droplet is a) 2 volts b) 5 volts c) 10 volts d) 15 volts?
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A drop of mercury is raised to a potential of 90 volts. This is broken into 27 identical drops. The potential of each droplet is a) 2 volts b) 5 volts c) 10 volts d) 15 volts? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A drop of mercury is raised to a potential of 90 volts. This is broken into 27 identical drops. The potential of each droplet is a) 2 volts b) 5 volts c) 10 volts d) 15 volts? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A drop of mercury is raised to a potential of 90 volts. This is broken into 27 identical drops. The potential of each droplet is a) 2 volts b) 5 volts c) 10 volts d) 15 volts?.
A drop of mercury is raised to a potential of 90 volts. This is broken into 27 identical drops. The potential of each droplet is a) 2 volts b) 5 volts c) 10 volts d) 15 volts? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A drop of mercury is raised to a potential of 90 volts. This is broken into 27 identical drops. The potential of each droplet is a) 2 volts b) 5 volts c) 10 volts d) 15 volts? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A drop of mercury is raised to a potential of 90 volts. This is broken into 27 identical drops. The potential of each droplet is a) 2 volts b) 5 volts c) 10 volts d) 15 volts?.
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