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Question

Two pendulums whose lengths differ by 11 cm oscillate at the same place so that one of them makes 30 oscillations and the other 36 oscillations during same time. Find the lengths of the pendulum.

A
36 cm and 25 cm
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B
37 cm and 26 cm
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C
25 cm and 14 cm
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D
30 cm and 19 cm
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Solution

The correct option is A 36 cm and 25 cm
Given,
l1l2=11 cm ...(1)
Pendulum 1 makes 30 oscillations and pendulum 2 makes 36 oscillations during same time.
Let T1 and T2 are the time period of pendulum (1) and (2) respectively.
30×T1=36×T2
30×2πl1g=36×2πl2g
l1l2=36×3630×30=3625
from (1)
l1l21=36251
l1l2l2=1125
11l2=1125
l2=25 cm
l1=36 cm

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