If the tip of pendulum covers a distance of 66 cm in complete oscillation, what is the angle described by pendulum at the centre?

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Solution

Q.
A pendulum clock uses a swinging weight as its timekeeping element. Invented in 1656 by Christiaan Huygens, the pendulum clock was the most precise timekeeper in the world, which is why it became so widely used. Its accuracy helped support the faster pace of life necessary for the Industrial Revolution. By the 1930s and 40s, home pendulum clocks were largely replaced by more affordable synchronous electric clocks. Today, pendulum clocks are mostly valued for their decorative and antique qualities.

Dhaani bought a pendulum clock for her living room. The clock features a small pendulum with a length of 45 cm. The minute hand is 14 cm long, while the hour hand is 6 cm long.

Based on the above information, answer the following questions

(iii) (b) If the tip of pendulum covers a distance of 66 cm in complete oscillation, what is the angle described by pendulum at the centre

1 $44 °$

2 $39 °$

3 $42 °$

4 $40 °$

Ans.
(3)

Length of the pendulum

$r = 45 c m L e t θ b e t h e a n g l e d e s c r i b e d b y p e n d u l u m a t t h e c e n t r e D i s \tan c e c o v e r e d b y a p e n d u l u m i n c o m p l e t e o s c i l l a t i o n = 2 \times \frac{θ}{360 °} \times 2 π r G i v e n d i s \tan c e = 66 c m 66 = 2 \times \frac{θ}{360 °} \times 2 \times \frac{22}{7} \times 45 66 = \frac{88 \times 45}{7 \times 360 °} \times θ 66 = \frac{11}{7} θ θ = \frac{66 \times 7}{11} = 42 °$

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