Answer :
The angular frequency of oscillation of the cylinder is about 8.106 rad/s.
What is Density?
Density is a physical property of matter that describes the amount of mass per unit volume of a substance. It is calculated as the mass of a substance divided by its volume. The standard unit of density is kilograms per cubic meter (kg/m^3), but it can also be expressed in grams per cubic centimeter (g/cm^3) or other units of mass and volume.
To find the angular frequency of oscillation of the cylinder, we need to use the formula for the period of oscillation of a submerged cylinder in a liquid:
T = 2π * sqrt(I / (mga))
where T is the period of oscillation, I is the moment of inertia of the cylinder about its axis of rotation, m is the mass of the cylinder, g is the acceleration due to gravity, and a is the cross-sectional area of the cylinder.
The moment of inertia of a solid cylinder about its axis of rotation is given by:
I = (1/2) * m * r^2
where r is the radius of the cylinder. In this case, the cross-sectional area of the cylinder is given, so we can find the radius using the formula:
A = π * r^2
Solving for r, we get:
r = sqrt(A/π) = sqrt((2.29 x 10^-1 m^2) / π) = 0.2706 m
So the moment of inertia of the cylinder is:
I = (1/2) * m * r^2 = (1/2) * (118 kg) * (0.2706 m)^2 = 4.378 kg*m^2
Now we can use the formula for the period of oscillation to find the angular frequency:
T = 2π * sqrt(I / (mga))
T = 2π * sqrt(4.378 kg*m^2 / ((118 kg) * (9.81 m/s^2) * (2.29 x 10^-1 m^2)))
T = 2π * sqrt(0.01915)
T = 0.775 s
The angular frequency is the reciprocal of the period:
ω = 2π / T = 2π / 0.775 s ≈ 8.106 rad/s
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