Question

A load of 20N on a wire of cross sectional area 8×10^7m^2 produces an extension of 10^4m. Calculate Young Modulus material of the wire if its length is 3m

Answer 1

Correct Question

A load of 20N on a wire of cross sectional area 8×10⁻⁷ m² produces an extension of 10⁻⁴m. Calculate Young Modulus material of the wire if its length is 3 m.

Given:

Force applied on wire, F= 20 N

Area of wire, A= 8×10⁻⁷ m²

Extension produced in wire, Δl= 10⁻⁴ m

Original length of wire, l= 3 m

To Find:

Young's Modulus of material of the wire

Solution:

We know that,

• Young's Modulus Y of material of a wire is given by

$\pink{\boxed{\bf{Y=\dfrac{F.l}{A.\triangle l}}}}$

where,

F is force applied on wire

l is original of wire

A is cross-sectional area of wire

Δl is change in length of wire

$\rule{190}{1}$

Le the the Young's Modulus of material of given wire be Y

So,

$\longrightarrow\rm{Y=\dfrac{F.l}{A.\triangle l}}$

$\longrightarrow\rm{Y=\dfrac{20\times3}{8\times10^{-7}\times10^{-4}}}$

$\longrightarrow\rm{Y=\dfrac{60}{8\times10^{-11}}}$

$\longrightarrow\rm\green{Y=7.5\times10^{11}\:N/m^{2}}$

Hence, the Young's Modulus of material of the wire is 7.5×10¹¹ N/m².