A steel rod has radius 50 mm and length 2 m. It is stretched along its length with a force of 400 KN. This causes an elongation of 0.5 mm. Find the (approximate) Young's modulus of steel from this information. 

Options

A. `2 xx 10^(10) N m^2`
B. `10^(11) N m^(2)`
C. `2xx 10^(11) N m^2`
D. `10^(12) N m^2`

Answer

C

Explanation

Elongation , `DeltaL = ((F/A)L)/(Y)`
`(F)/(A) = (400xx 10^3)/(pi(50xx 10^(-3))^2) (therefore A = pi r^2)`
`= 50.92 xx 10^6`
`rArr Y = (50.92xx 10^6 xx 2)/(0.5 xx 10^(-3))`
`therefore Y = 2.03 xx 10^(11) Nm^2`