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The bob of a pendulum has mass of 40 mg and charge 9 = 10 µC Is given to it, length of pendulum is 90 cm The point of suspension support also has a point charge of 10 µC. What is the time period of oscillation of pendulum?
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The bob of a pendulum has mass of 40 mg and charge 9 = 10 µC Is given ...
The Time Period of an Oscillating Pendulum with Charged Bob
Given:
- Mass of the bob (m) = 40 mg = 40 × 10^-6 kg
- Charge of the bob (q) = 9 × 10^-6 C
- Length of the pendulum (L) = 90 cm = 0.9 m
- Charge of the point of suspension (Q) = 10 × 10^-6 C
Formula:
The formula for the time period (T) of an oscillating pendulum is given by:
T = 2π√(L/g)
Where:
- T is the time period of the pendulum
- L is the length of the pendulum
- g is the acceleration due to gravity
Calculating the Time Period:
1. Calculate the acceleration due to gravity (g):
- The value of g is approximately 9.8 m/s^2.
2. Calculate the effective length (L') of the pendulum:
- The effective length of the pendulum takes into account the electric repulsion between the bob and the point of suspension.
- The effective length can be calculated using the following formula:
L' = L + (kqQ)/(4πε₀mg)
Where:
- k is the Coulomb's constant (9 × 10^9 Nm^2/C^2)
- ε₀ is the permittivity of free space (8.854 × 10^-12 C^2/Nm^2)
3. Substitute the values of L' and g into the formula for the time period:
- T = 2π√(L'/g)
4. Calculate the time period (T) using the above formula.
Summary:
The time period of an oscillating pendulum with a charged bob can be calculated by considering the effective length of the pendulum, which takes into account the electric repulsion between the bob and the point of suspension. Using the formula T = 2π√(L'/g), where L' is the effective length and g is the acceleration due to gravity, we can find the time period of the pendulum.
Given:
- Mass of the bob (m) = 40 mg = 40 × 10^-6 kg
- Charge of the bob (q) = 9 × 10^-6 C
- Length of the pendulum (L) = 90 cm = 0.9 m
- Charge of the point of suspension (Q) = 10 × 10^-6 C
Formula:
The formula for the time period (T) of an oscillating pendulum is given by:
T = 2π√(L/g)
Where:
- T is the time period of the pendulum
- L is the length of the pendulum
- g is the acceleration due to gravity
Calculating the Time Period:
1. Calculate the acceleration due to gravity (g):
- The value of g is approximately 9.8 m/s^2.
2. Calculate the effective length (L') of the pendulum:
- The effective length of the pendulum takes into account the electric repulsion between the bob and the point of suspension.
- The effective length can be calculated using the following formula:
L' = L + (kqQ)/(4πε₀mg)
Where:
- k is the Coulomb's constant (9 × 10^9 Nm^2/C^2)
- ε₀ is the permittivity of free space (8.854 × 10^-12 C^2/Nm^2)
3. Substitute the values of L' and g into the formula for the time period:
- T = 2π√(L'/g)
4. Calculate the time period (T) using the above formula.
Summary:
The time period of an oscillating pendulum with a charged bob can be calculated by considering the effective length of the pendulum, which takes into account the electric repulsion between the bob and the point of suspension. Using the formula T = 2π√(L'/g), where L' is the effective length and g is the acceleration due to gravity, we can find the time period of the pendulum.
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The bob of a pendulum has mass of 40 mg and charge 9 = 10 µC Is given ...
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The bob of a pendulum has mass of 40 mg and charge 9 = 10 µC Is given to it, length of pendulum is 90 cm The point of suspension support also has a point charge of 10 µC. What is the time period of oscillation of pendulum?
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The bob of a pendulum has mass of 40 mg and charge 9 = 10 µC Is given to it, length of pendulum is 90 cm The point of suspension support also has a point charge of 10 µC. What is the time period of oscillation of pendulum? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The bob of a pendulum has mass of 40 mg and charge 9 = 10 µC Is given to it, length of pendulum is 90 cm The point of suspension support also has a point charge of 10 µC. What is the time period of oscillation of pendulum? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The bob of a pendulum has mass of 40 mg and charge 9 = 10 µC Is given to it, length of pendulum is 90 cm The point of suspension support also has a point charge of 10 µC. What is the time period of oscillation of pendulum?.
The bob of a pendulum has mass of 40 mg and charge 9 = 10 µC Is given to it, length of pendulum is 90 cm The point of suspension support also has a point charge of 10 µC. What is the time period of oscillation of pendulum? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The bob of a pendulum has mass of 40 mg and charge 9 = 10 µC Is given to it, length of pendulum is 90 cm The point of suspension support also has a point charge of 10 µC. What is the time period of oscillation of pendulum? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The bob of a pendulum has mass of 40 mg and charge 9 = 10 µC Is given to it, length of pendulum is 90 cm The point of suspension support also has a point charge of 10 µC. What is the time period of oscillation of pendulum?.
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