Question

a elastic belt is placed round the rim of pulley of radius 5cm .one point on belt is pulled dire tly away from the centre o of the pulley until it is at p10cm from o.find lenght of belt that is in contact with rim of pulley

Answer 1

Solution: We know that except arc AB, complete circle is in contact with rim.

Length of arc AB = ∅/360° × 2πR

Now we know that cos∅ = Base/Hypotenuse

→ cos∅ = 5/10 → cos∅ = ½ = cos 60°

Hence value of single ∅ is 60°

Then value of angle AOB i.e., complete ∅ = 60° + 60° = 120°

→ l of arc(AB) = 120°/360° × 2π × 5

→ ⅓ × 10π → 10π/3

L of rim not attached with belt = Circumference of circle - l of arc(AB)

→ 2π × 5 - 10π/3

→ 10π - (10π/3)

→ 20π/3

Hence 20π/3 cm of rim is not attached with belt.

Answer 2

See the attachment below

Hope it helps

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