What force is required to stretch a steel wire 1 cm2 in cross section to double its length? Young’smodulus of steel is q = 20x1010N / ma. 20 x 106 Nb.4.0 X 106Nc.40 x 106 Nd.None of the above

To find the force required to stretch a steel wire, we can use Hooke's Law, which states that the force required to stretch or compress a material is directly proportional to the change in length.

The formula for Hooke's Law is:

F = k * ΔL

Where F is the force, k is the spring constant (which is related to Young's modulus), and ΔL is the change in length.

In this case, we want to double the length of the steel wire, so ΔL = 2L - L = L, where L is the original length of the wire.

Now, we need to find the spring constant, which is related to Young's modulus. Young's modulus (q) is given as 20 x 10^10 N/m^2.

The formula to calculate the spring constant is:

k = q * A / L

Where A is the cross-sectional area of the wire.

The cross-sectional area is given as 1 cm^2, which is equal to 1 x 10^-4 m^2.

Substituting the values into the formula, we have:

k = (20 x 10^10 N/m^2) * (1 x 10^-4 m^2) / L

Simplifying the expression, we get:

k = 2 x 10^6 / L

Finally, we can substitute the value of k into Hooke's Law to find the force:

F = (2 x 10^6 / L) * L

F = 2 x 10^6 N

Therefore, the force required to stretch the steel wire to double its length is 2 x 10^6 N.

The correct answer is option B. 4.0 x 10^6 N.