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Determine the period of small oscillations of a simple pendulum that is a bob suspended by a thread l= 20cm in length if it is located in a liquid whose density is n=3 times less than that of the bob. The resistance of the liquid is to be neglected?
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- **Given Data**

- Length of pendulum, l = 20 cm
- Density of liquid = 1/3 * density of bob
- Negligible resistance of liquid

- **Formula for Period of Small Oscillations**

The period (T) of small oscillations of a simple pendulum is given by the formula:

T = 2π√(l/g)

where:

- l is the length of the pendulum
- g is the acceleration due to gravity

- **Adjusting for Density of Liquid**

In a liquid with density 1/3 times less than that of the bob, the effective length of the pendulum will be the sum of the actual length and a fraction of the displaced liquid length. The fraction is calculated by taking the ratio of densities (3:1).

Therefore, the effective length (l') of the pendulum in the liquid will be:

l' = l + (1/3)l = 4/3 * l

- **Calculating the Period**

Substituting the effective length into the formula for the period of small oscillations:

T' = 2π√(4/3 * l / g)
= 2π√(4/3) * √(l/g)
= (2/√3)π√(l/g)

Therefore, the period of small oscillations of the simple pendulum in the given liquid is (2/√3) times the original period in air.
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Determine the period of small oscillations of a simple pendulum that is a bob suspended by a thread l= 20cm in length if it is located in a liquid whose density is n=3 times less than that of the bob. The resistance of the liquid is to be neglected?
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