There are two wires of same material. Their radii and lengths are both in the ratio `1:2.` If the extensions produced are equal, what is the ratio of the loads?

Explanation

Ratio of lengths, `l_(1):l_(2)=1:2`
Ratio of radii, `r_(1):1_(2)-1:2`
Made of same material `rArrY_(1)=Y_(2)`
Ratio of loads `m_(1):m_(2)=?`
Use `Y=(mg)/(pir^(2))(l)/(e)` then
`(m_(1))/(m_(2))=(Y_(1)r_(1)^(2)l_(2))/(l_(1)Y_(2)r_(2)^(2))=(1xx2)/(1xx2^(2))=(1)/(2)`
`thereforem_(1):m_(2)=1:2`