A pendulum of $28$ cm length oscillates such that its string makes an angle of $30^{o}$ with the vertical when it is at one of the extreme positions. Find the ratio of the distance to the displacement of the bob of the pendulum when it moves from one extreme position to other.

22 : 21

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42 : 21

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1 : 1

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43 : 22

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Solution

The correct option is A $22 : 21$
The pendulum moves from extreme end A to extreme end C.
As shown in the figure, $Distance = \frac{60}{360} \times 2 π R = \frac{π R}{3}$ , Where $R$ is the length of the pendulum.
$Displacement = 2 R s i n (30^{o}) = R$ ,
$∴$ $\frac{Distance}{Displacement} = \frac{\frac{π R}{3}}{R} = \frac{π}{3} = \frac{22}{21}$

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A pendulum of 28 cm length oscillates such that its string makes an angle of 30o with the vertical when it is at one of the extreme positions. Find the ratio of the distance to the displacement of the bob of the pendulum when it moves from one extreme position to other.

The correct option is A 22:21The pendulum moves from extreme end A to extreme end C.As shown in the figure, Distance=60360×2πR=πR3, Where R is the length of the pendulum.Displacement=2Rsin(30o)=R,∴ DistanceDisplacement=πR3R=π3=2221

A pendulum of $28$ cm length oscillates such that its string makes an angle of $30^{o}$ with the vertical when it is at one of the extreme positions. Find the ratio of the distance to the displacement of the bob of the pendulum when it moves from one extreme position to other.