Question

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

पर्याय

• `25/64`

• `64/25`

• `8/5`

• `5/4`

Answer 1

Two simple pendulums A and B are made to oscillate simultaneously and it is found that A completes 10 oscillations in 20 sec and B completes 8 oscillations in 10 sec. The ratio of the lengths of A and B is `64/25`.

Explanation:

`"T"_"A" = 20/10 = 2  "s"`

`"T"_"B" = 10/8 = 1.25  "s"`

`"But"  "T" prop sqrtl`

`therefore "T"_"A"/"T"_"B" = sqrt(l_"A"/l_"B")`

`therefore l_"A"/l_"B" = "T"_"A"^2/"T"_"B"^2 = 2^2/1.25^2`

`l_"A"/l_"B" = 64/25`