Two pendulums whose lengths differ by 11cm 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
36cm and 25cm
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B
37cm and 26cm
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C
25cm and 14cm
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D
30cm and 19cm
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Solution
The correct option is A36cm and 25cm Given, l1−l2=11cm...(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 ⇒30×2π√l1g=36×2π√l2g ⇒l1l2=36×3630×30=3625 from (1) l1l2−1=3625−1 ⇒l1−l2l2=1125 ⇒11l2=1125 ⇒l2=25cm ⇒l1=36cm