Four identical rods are stretched by same force. Maximum extension is produced in

Options

A. L = 10 cm, D = 1 mm
B. L = 100 cm, D = 2 mm
C. L = 200 cm, D = 3 mm
D. L = 300 cm, D = 4 mm

Answer

b

Explanation

When strain is small, the ratio of the longitudinal stess to the corresponding longitudianl strain is called Young's modulus of the material of the body.
`Y = ("Stress")/("strain") = (F//A)/(I//L)`
`implies I prop (L)/(A) prop (L)/(pi r^(2)) prop (L)/(D^(2))`
(a) `(L)/(D^(2)) =(10)/((1 xx 10^(-1)^(2)) = (10)/(10^(-2)) = 1 xx 10^(3)`
(b) `(L)/(D^(2)) = (100)/((2 xx 10^(-1))^(2)) = (100)/(4xx 10^(-2)) = 25 xx 10^(2)`
(c ) `(L)/(D^(2)) = (200)/((3 xx 10^(-1))^(2)) = 22 xx 10^(2) = 2.2 xx 10^(3)`
(d) `(L)/(D^(2)) = (300)/((4 xx 10^(-1))^(2)) = 18.75 xx 10^(2) = 1.875 xx 10^(3)`
Hence, maximum extension is prouduced in second case i.e., in option (b)