A pendulum of length 40cm swings through an

Blitzo

Blitzo

Answered question

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 .

Answer & Explanation

xleb123

xleb123

Skilled2023-06-03Added 181 answers

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:
Arc Length=θ×r
where θ 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 π radians in 180 degrees, we can use the conversion factor:
1 degree=π180 radians
So, 20 degrees in radians is:
20×(π180)
Next, we substitute the values into the formula for arc length:
Arc Length=(20×π180)×40
Simplifying the expression:
Arc Length=20π180×40
Further simplification:
Arc Length=2π9×40
Calculating the value:
Arc Length=80π9
Therefore, the arc length moved by the pendulum in one swing is 80π9 cm.

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