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Two pendulums differ in lengths by 22 cm...

Two pendulums differ in lengths by 22 cm. They oscillate at the same place so that one of them makes 30 oscillations and the other makes 36 oscillations during the same time. The lengths (in cm) of the pendulums are

A

72 and 50

B

60 and 38

C

50 and 28

D

80 and 58

Text Solution

Verified by Experts

The correct Answer is:
A
`T_(1)=2pisqrt((l_(1))/(g))`
`T_(2)=2pisqrt((l_(2))/(g))`
`(t)/(T_(1))=30 (T_(2))/(T_(1))=(5)/(6)`
`(t)/(T_(2))=36 6T_(2)=5T_(1)`
`T_(1)^(2)=(88)/(100)xx(36)/(11)~~(6xxsqrt(2))/(10)=(6sqrt(2))/(5)`
`(6sqrt(2))/(5)=2pi sqrt((l_(1))/(g))`
`(36xx2)/(25)=4xx10xx(l_(1))/(10) Ans. (A)`
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