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

Options

A. 72 and 50
B. 60 and 38
C. 50 and 28
D. 80 and 58

Answer

A

Explanation

`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)`