Question

16
An iron wire and a brass wire, of equal lengths and equal cross-sectional areas, are joined at
one end. A tensile force F is applied to the free ends, as shown.
iron
brass
If the Young modulus of iron is twice that of brass, which statement is true?
The extension of the brass wire is twice that of the iron wire.
The extension of the iron wire is twice that of the brass wire.
The tension in the brass wire is twice that in the iron wire.
The tension in the iron wire is twice that in the brass wire.

Answer 1

Given :

Length of iron and brass wire = L

Area of cross-section of iron and brass wire = A

Force applied =F

To Find :

The extension produced in brass and iron wires

Solution :

• Young's modulus is given by the formula

           $Y = \frac{FL}{Ae}$

           $e = \frac{FL}{AY}$

• The extension produced in brass wire is

          $e_{brass} = \frac{FL}{AY}\rightarrow Equation(1)$

• The extension produced in iron wire is

          $e_{iron} = \frac{FL}{A(2Y)}$

          $e_{iron} = \frac{FL}{2AY}\rightarrow Equation (2)$

• From equations (1) and (2)

         $e_{brass} = 2\times e_{iron}$

The extension produced in brass wire is more i.e., twice that of iron wire