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

Explanation

Data` Y_(1)/Y_(2) = 1, L_(1)/L_(2) , r_(1)/r_(2) = 1/2 , (DeltaL_(1))/(DeltaL_(2)) =1`
`Y = (Mg//pir^(2))/(DeltaL//L) = (MgL)/(pir^(2)DeltaL)" " M =(Ypir^(2)DeltaL)/(gL)`
` M_(1) = (Y_(1)pir_(1)^(2) DeltaL_(1))/(gL_(1)) and M_(2) = (Y_(2)pir_(2)^(2)DeltaL_(2))/(gL_(2))`
` M_(1)/M_(2) = Y_(1)/Y_(2) xx (r_1/r_(2))^(2) xx ((DeltaL_(1))/(DeltaL_(2))) xx L_(2)/L_(1)`
` = 1xx(1/2)^(2) xx 1xx2`
The ratio of the loads, ` M_(1)/M_(2) =1/2`