Two simple pendulums A and B are made to oscillate simultaneously and it is found that A completes 10 oscillations in 20 sand B completes 8 oscillations in 10 s. The ratio of the lengths of A and B is

Options

A. `(8)/(5)`
B. `(64)/(25)`
C. `(5)/(4)`
D. `(25)/(64)`

Answer

B

Explanation

According to questions,
For pendulum A,
`T_(A) = 2pi sqrt((I_(A))/(g))`
`(20)/(10)=2pi sqrt((I_(A))/(g))`
For pendulum B,
`T_(B)=2pi sqrt((I_(B))/(g))`
`(10)/(8)=2pi sqrt((I_(B))/(g))`
Dividing Eq. (i) by Eq. (ii), we get
`(I_(A))/(I_(B))=((160)/(100))^(2)`
`(I_(A))/(I_(B))=(64)/(25)`