Question

1. (i)Two pendulums A and B have length 2 m and 0.5 m. Which pendulum will make more oscillations in one minute and why? (ii) What is the relation between time period (T) and frequency (f) of an oscillation of a simple pendulum?
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Answer 1

Answer:

Ｔｉｍｅ ｐｅｒｉｏｄ ｏｆ

ｏｓｃｉｌｌａｔｉｏｎ

ｏｆ ａ ｓｉｍｐｌｅ ｐｅｎｄｕｌｕｍ

ｉｓ ｇｉｖｅｎ ｂｙ:

Ｔ=2π√ ｌ/ｇ∝ √ｌ

Ｔｈｕｓ, ｔｈｅ ｒａｔｉｏ ｏｆ ｔｈｅｉｒ ｔｉｍｅ ｐｅｒｉｏｄｓ ｉｓ Ｔ1/Ｔ2 =√0.5/2

= 1/2

⟹Ｔ 2 =2Ｔ 1

Ｔｈｕｓ, ｔｈｅ ｓｈｏｒｔｅｒ

ｐｅｎｄｕｌｕｍ ｗｏｕｌｄ ｈａｖｅ ｃｏｍｐｌｅｔｅｄ ｅｘａｃｔｌｙ 2 ｏｓｃｉｌｌａｔｉｏｎｓ

ｗｈｅｎ ｔｈｅ ｌｏｎｇｅｒ ｐｅｎｄｕｌｕｍ ｗｏｕｌｄ ｈａｖｅ ｃｏｍｐｌｅｔｅｄ ｔｈｅ ｆｉｒｓｔ ｏｓｃｉｌｌａｔｉｏｎ.

Explanation:

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