When a load of 80N is suspended from a string, its length is 101mm. If a load of 100N is suspended , its length is 102mm. If a load of 160N is suspended from it, then length of the string is (Assume the area of cross-section unchanged)

Options

A. 15.5cm
B. 13.5cm
C. 16.5cm
D. 10.5cm

Answer

D

Explanation

`T_1 =80N`
`L_1 =101 mm`
`T_(2)= 100 N`
`L_2 =102 mm`
`T_(3) =160 N`.
`L_(3) = ?`
`(l) =(l^2 T_2 -l_2 T_1)/(T_2 - T_1)`
`=(101xx100 - 102 xx 80)/(100-80)`
`=(101xx100)/(20)-(102xx80)/(20)`.
`=505 -408=97 cm`.
`(T_1)/(T_3)=(4)/(l_3 -97)` .
`=(80)/(160)-(4)/(l_3 -97)`
`rArr l_3 -97 =8`
`rArr l_3 =8 +97=105 mm ( or ) 10.5 cm`.