An uniform sphere is at rest and in equilibrium with the help of two vertical strings of unequal length larger string has length `'2l'` and shorter has length `('7l')/(5)`. Both strings and centre of sphere are in one plane.

Radius of sphere is `l`. If ratio of fundamental frequancy in longer wire to shorter wire is `k` then `5sqrt(5k)` is (both strings are of same material)

Answer

7

Explanation

An uniform………….

`T_(1)l=T_(2)((4l)/(5))`
`5T_(1)=4T_(2)`
`k = (f_(1))/(f_(2)) = sqrt((T_(1))/(T_(2))).(l_(2))/(l_(1))`
`= sqrt((4)/(5)).(7)/(10) = (7)/(5sqrt(5))`