Blitzo

2022-08-05

A pendulum of length 40cm swings through an angle of 20degrees . Calculate the arc length PQ moved by the pendulum in one swing .

xleb123

To calculate the arc length moved by the pendulum in one swing, we can use the formula for the arc length of a circle sector.
The formula for the arc length is given by:

where $\theta$ is the angle in radians and $r$ is the radius of the circle.
In this case, the length of the pendulum (radius of the circle) is given as 40 cm, and the angle through which it swings is 20 degrees.
First, we need to convert the angle from degrees to radians. Since there are $\pi$ radians in 180 degrees, we can use the conversion factor:

So, 20 degrees in radians is:
$20×\left(\frac{\pi }{180}\right)$
Next, we substitute the values into the formula for arc length:

Simplifying the expression:

Further simplification:

Calculating the value:

Therefore, the arc length moved by the pendulum in one swing is $\frac{80\pi }{9}$ cm.

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