Question

A solid steel rod is 4m long and 9cm in diameter. What will be its decrease in length when carrying a load of 80000kg, take the young's modulus, E = 1.9 x 10¹ Pa​

Answer 1

The decrease in length of a solid steel rod under load can be calculated using the formula:

ΔL = (F * L) / (A * E)

where:
ΔL = the change in length of the rod
F = the force applied to the rod (in newtons)
L = the original length of the rod (in meters)
A = the cross-sectional area of the rod (in square meters)
E = the Young's modulus of the material (in pascals)

First, we need to calculate the cross-sectional area of the rod:

r = d/2 = 0.09/2 = 0.045 m
A = π * r^2 = 3.14 * 0.045^2 = 0.0064 m^2

Next, we can calculate the force applied to the rod:

F = m * g = 80000 * 9.8 = 784000 N

Now we can substitute these values into the formula:

ΔL = (F * L) / (A * E) = (784000 * 4) / (0.0064 * 1.9e11) = 0.000052 m

Therefore, the decrease in length of the steel rod when carrying a load of 80000 kg is approximately 0.000052 meters or 0.052 millimeters.