The second moment of area of a hollow cylindrical beam with an inner radius of 18mm and an outer radius of 20mm is equal to
A) 2.7x10-9m 4
B) 4.3x10-8 m 4
C) 7.9x10 - 13m 4
D) 2.7x10 3 m 4
J=π(D²-d²)/32 =...
To find the second moment of area (also known as the moment of inertia) of a hollow cylindrical beam, we can use the formula:
I = π/4 * (d₂^4 - d₁^4)
where I is the second moment of area, π is a mathematical constant approximately equal to 3.14159, and d₁ and d₂ are the inner and outer diameters of the cylindrical beam, respectively.
In this case, we are given the inner and outer radii instead of the diameters. To convert the radii to diameters, we multiply them by 2.
Inner diameter (d₁) = 2 * 18mm = 36mm
Outer diameter (d₂) = 2 * 20mm = 40mm
Now, substituting the values into the formula, we get:
I = π/4 * (40^4 - 36^4)
Calculating this expression gives us:
I ≈ π/4 * (2560000 - 1297464)
I ≈ π/4 * 1262536
I ≈ 990967.771
Now, we can compare this value with the given options:
A) 2.7x10^-9 m^4
B) 4.3x10^-8 m^4
C) 7.9x10^-13 m^4
D) 2.7x10^3 m^4
Comparing the calculated value of I with the options, we can see that none of the options match. Double-check your calculations or verify if there is a typo in the options provided.