Consider a string which is suspended from the ceiling. The length of the string is 98 mm when a load of 60 N is suspended from a string and the length of the string is 102 mm when a load of 100 N is suspended from a string. If the area of cross-section is unchanged in the entire process, what is the length (in cm) of the string when a load of 150 N is suspended?

Answer

`10.70`

Explanation

Extension, `I=(mgL)/(AY)`
For same wire stretched under different loads,
`(l_(1))/(l_(2)) =(M_(1)g)/( M_(2)g)`
Given : `L +l_(1) = 98mn = 9.8cm`
`L+l_(2) =102 mm = 10.2 cm`
`:.(l_(1))/(l_(2)) = (9.8-L)/(10.2-L)`
`:.(9.8-L)/( 10.2-L) = (60)/(100) = (3)/(5)`
`:. 49 - 5L = 30.6 -3L`
`:. 2 L = 18.4 rArr L =9.2 cm`
Let length of wire be 13 when load of 150 N is suspended from it.
`:.` extension `I_(3) = L_(3) -L`
Now, `(l_(1))/(l_(1)) =(L_(3)-L)/(9.8-L) =(L_(3)-9.2)/( 9.8-9.2) =(L_(3) -9.2)/( 0.6)`
But `(l_(1))/(l_(1)) = (M_(2)g)/( M_(1)g) =(150)/(60)`
`:. (L_(3)-9.2)/( 0.6) =(150)/(60)`
`:.L_(3) -9.2 =(150 xx 0.6)/(60) =1.5 `
`:.L_(3) =1.5 +9.2 =10.7 cm`