# A pendulum swings through an angle of 30 and describes an arc 17.6 cm in length.Find the length of pendulum.​

A pendulum swings through an angle of 30 and describes an arc 17.6 cm in length.
Find the length of pendulum.​

### 2 thoughts on “A pendulum swings through an angle of 30 and describes an arc 17.6 cm in length.<br />Find the length of pendulum.​”

1. Given

• θ = 30°
• Arc length = 17.6 cm

To Find

• Length of the pendulum

Solution

☯ θ/360 × 2πr = arc length

• Here in the given case, the value of θ is 30°

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✭ According to the Question :

➞ θ/360 × 2πr = arc length

➞ 30/360 × 2 × 22/7 × r = 17.6

➞ 1/12 × 2 × r = 17.6 × 7/22

➞ 1/6 × r = 5.6

➞ r = 5.6 × 6

➞ r = 33.6 cm

∴ The length of the pendulum is 33.6 cm

2. ## Given :-

A pendulum swings through an angle of 30 and describes an arc 17.6 cm in length.

## To Find :-

Length of pendulum

## Solution :-

At first

We know that

$$\sf Perimeter \; of \; circle = 2\pi r$$

$$\sf \dfrac{\theta}{360} \times 2\pi r$$

$$\sf \dfrac{30}{360} \times 2(3.14)r = 17.6$$

$$\sf\dfrac{1}{12} \times 6.28r = 17.6$$

$$\sf 6.28r = 12(17.6)$$

$$\sf r = \dfrac{211.2}{6.28}$$

$$\sf r = 33.6 cm$$