The diameter of a brass rod is 0.2 mm and Young’s modulus of brass is 9 x 1010 N/m2. The force required to stretch by 1% of its length is kππ newton. Find k.

To solve this problem, we need to use the formula for stress and strain.

Stress is defined as the force per unit area, and strain is defined as the change in length divided by the original length.

The formula for stress is: Stress = Force / Area

The formula for strain is: Strain = ΔLength / Original Length

Given that the strain is 1% or 0.01 (since 1% = 1/100 = 0.01), and the original length is not given but it will be cancelled out in the equation, we can ignore it.

We also know that stress = Young's Modulus * strain.

We can substitute the stress in the above equation with Force / Area, and we get: Force / Area = Young's Modulus * strain

Rearranging for Force gives us: Force = Area * Young's Modulus * strain

The area of the rod can be found using the formula for the area of a circle (since the cross section of the rod is a circle), which is π*(d/2)^2. The diameter d is given as 0.2 mm, which is 0.2 * 10^-3 m.

Substituting these values in, we get:

Force = π*(0.2 * 10^-3 /2)^2 * 9 * 10^10 N/m^2 * 0.01

Solving this gives us:

Force = π * (10^-4) m^2 * 9 * 10^10 N/m^2 * 0.01 = π * 9 * 10^6 N

So, the force required to stretch the brass rod by 1% of its length is 9π * 10^6 Newton. Therefore, k = 9 * 10^6.