Question

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☛ Find the ɑngle in rɑdiɑn through which ɑ pendulum swings if its length is 75 cm ɑnd the tip describes ɑn ɑrc of length
1 ]. 10 cm
2]. 15 cm
3]. 21 cm

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Answer 1

Answers:-

• 1) 0.14 radians.

• 2) 0.2 radians.

• 3) 0.28 radians.

Explanation:-

Given:-

• Length of the pendulum = 75 cm.

To Find:-

• The angle in radians through which the pendulum swings at various points.

Relation Used:-

$\\ \bf\mapsto \theta = \dfrac{l}{r} .$

Where,

• $\theta$ is the angle in radians.
• l = length of the arc.
• r = radius of the arc.

Understanding of the que:-

We can observe that the whole system of the question can represent a part of the circle of radius = length of the pendulum and arc of all 3 cases. You can refer to attachment for better understanding (Sorry for my poor drawing ^^").

Case I:-

When the tip describes an arc of length 10 cm.

By Using The Relation,

$\\ \tt\mapsto \theta = \frac{l}{r} .$

$\\ \tt\mapsto \theta = \cancel{\frac{10 \: cm}{75 \: cm} }.$

$\\ \tt\mapsto \theta = \frac{2}{15} .$

$\\ \bf\mapsto \theta =0.1 \bar{3} \approx0.14 \: \: \rm radians.$

Case II:-

When the tip describes an arc of length 15 cm.

By Using The Relation,

$\\ \tt\mapsto \theta = \frac{l}{r} .$

$\\ \tt\mapsto \theta = \cancel{\frac{15 \: cm}{75 \: cm} }.$

$\\ \tt\mapsto \theta = \frac{1}{5} \: \rm radians.$

$\\ \bf\mapsto \theta =0.2 \: \: \rm radians.$

Case III:-

When the tip describes an arc of 21 cm.

By Using The Relation,

$\\ \tt\mapsto \theta = \frac{l}{r} .$

$\\ \tt\mapsto \theta = \cancel{\frac{21 \: cm}{75 \: cm}} \: \rm radians .$

$\\ \bf\mapsto \theta =0.28 \: \: \rm radians.$

Answer 2

Givben :-

ɑ pendulum swings if its length is 75 cm ɑnd the tip describes ɑn ɑrc of length

1]. 10 cm

2]. 15 cm

3]. 21 cm

To Find :-

Angle in radian

Solution :-

We know that

Angle in radian = Length of arc/Length of radius

1] 10 cm

Angle in radian = 10/75

Angle in radian = 2/15 radians

2] 15 cm

Angle in radian = 15/75

Angle in radian = 3/15

Angle in radian = 1/5 radians

3] 21 cm

Angle in radian = 21/75

Angle in radian = 7/25 raidans

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