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Sixty four spherical drops each of radius 2cm and carrying 5c charge combine to form a bigger drop ,its capacity is?
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Sixty four spherical drops each of radius 2cm and carrying 5c charge c...
Calculation of Capacity of Bigger Drop
Step 1: Calculation of Total Charge
- Each spherical drop has radius = 2cm and charge = 5c
- Volume of each drop = (4/3)πr³ = (4/3)π(2cm)³ = 32/3 π cm³
- Total volume of 64 drops = 64 × (32/3) π cm³ = 682.67 π cm³
- Total charge of 64 drops = 64 × 5c = 320c
Step 2: Calculation of Radius of Bigger Drop
- Let the radius of bigger drop be R
- Volume of bigger drop = (4/3)πR³
- Equating the volumes of 64 drops and bigger drop: (4/3)πR³ = 682.67 π cm³
- Solving for R, we get R = 8 cm
Step 3: Calculation of Capacity of Bigger Drop
- Capacity of a conductor is given by the formula: C = Q/V
- Where Q is charge and V is potential
- For a spherical conductor, capacity is given by the formula: C = 4πεR
- Where ε is the permittivity of free space and R is the radius of the conductor
- Substituting the values, we get C = 4 × π × 8 × ε = 32 π ε
- Using the value of permittivity of free space, ε = 8.85 × 10⁻¹² F/m
- Therefore, capacity of the bigger drop = 32 π × 8.85 × 10⁻¹² F/m = 8.84 × 10⁻¹⁰ F
Final Answer
Capacity of the bigger drop is 8.84 × 10⁻¹⁰ F.
Community Answer
Sixty four spherical drops each of radius 2cm and carrying 5c charge c...
The charge of the bigger drop will be
Q= 5 * 64= 320C
The radius of bigger drop
64^1/3 × 2cm= 8cm
The potential of bigger drop
KQ/R= 9×10^9 ×320/8×10^-2(for cm to m)
= 36×10^12
Capacity= Q/V
= 320/ 36×10^12
= 80/9 ×10^-12
Q= 5 * 64= 320C
The radius of bigger drop
64^1/3 × 2cm= 8cm
The potential of bigger drop
KQ/R= 9×10^9 ×320/8×10^-2(for cm to m)
= 36×10^12
Capacity= Q/V
= 320/ 36×10^12
= 80/9 ×10^-12
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Sixty four spherical drops each of radius 2cm and carrying 5c charge combine to form a bigger drop ,its capacity is?
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Sixty four spherical drops each of radius 2cm and carrying 5c charge combine to form a bigger drop ,its capacity is? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Sixty four spherical drops each of radius 2cm and carrying 5c charge combine to form a bigger drop ,its capacity is? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sixty four spherical drops each of radius 2cm and carrying 5c charge combine to form a bigger drop ,its capacity is?.
Sixty four spherical drops each of radius 2cm and carrying 5c charge combine to form a bigger drop ,its capacity is? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Sixty four spherical drops each of radius 2cm and carrying 5c charge combine to form a bigger drop ,its capacity is? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sixty four spherical drops each of radius 2cm and carrying 5c charge combine to form a bigger drop ,its capacity is?.
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