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

Answer

D

Explanation

Frequency of oscillations made by a simple pendulum of length l is `upsilon=(1)/(2pi)sqrt((g)/(l)) implies upsilon prop (1)/(sqrtl)`
Since, A completes 10 oscillations in 20 s
`implies upsilon_(A)=(10)/(20)=0.5 Hz` Similarly, `upsilon_(B)=(8)/(10)=0.8 Hz`
`:. (upsilon_(A))/(upsilon_(B))=(5)/(8)=sqrt((I_(B))/(I_(A)))` or `(I_(A))/(I_(B))=(64)/(25)`