Question

a wire of 1mm diameter and 1m long fixed at one end in stretched by 0.01mm. when a load of 10kg is attached to its free end. calculate the young's modulus​

Answer 1

Find the stress, strain and Young's modulus of the material of the ... The wire is stretched by 0.1 cm. .... 1 mm² = 1 × 10- 6 m², Load attached = F = 10 kg-wt = 10 ...

Answer 2

The young's modulus​ of the wire is $1.25\times10^1^3N/m^2$.

Explanation:

The formula for young's modulus​ is given as

$Y=\frac{Fl}{Ax}$

Here, F is the force applied on the wire, A is the cross-sectional area of the wire, l is the initial length and x is the change in the length of the wire.

Given l = 1 m, $x = 0.01 mm =1\times10^-^5m$, $A=\pi r^2=\pi\times(0.5\times10^-^3)^2=25\pi\times 10^8m$.

Force is given as

F = mg

g is acceleration due to gravity.

F = 10 kg x 9.8 m/s^2

F = 98 N.

substitute the given values, we get

$Y=\frac{98\times 1}{25\times3.14\times10^-^8\times10^-^5}$

$Y=1.25\times10^1^3N/m^2$

Thus, the young's modulus​ of the wire is $1.25\times10^1^3N/m^2$.

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