
The moment of inertia of a hollow cylinder of mass and inner radius and outer radius about its central axis is
(A).
(B).
(C).
(D).
Answer
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Hint: You can start the solution by calculating the mass per unit cross section area. Then divide the cylinder into an inner and outer cylinder. Then find the mass of the inner and outer cylinder by using the equation . Then use the equation to find the moment of inertia of the inner and the outer cylinder. Then calculate the difference between the moment of the inertia of the outer and inner cylinder to reach the solution.
Complete step-by-step answer:
Here we are given a hollow cylinder with a mass and inner radius and outer radius .
So the total area of cross section of the cylinder is
Area
The mass of the hollow cylinder is distributed over a cross section area of .
So the mass per unit cross section area is
In this problem we have a hollow cylinder, let’s divide it into two parts: a bigger cylinder with a radius and a smaller cylinder with a radius .
The mass of the outer cylinder is
Similarly the mass of inner cylinder is
The moment of inertia of the outer cylinder is
The moment of inertia of the inner cylinder is
The net moment of inertia is the difference in the moment of inertia of the outer cylinder and the movement of inertia of the inner cylinder
Hence, option B is the correct choice.
Note: In this problem we divided the hollow cylinder into an outer bigger cylinder and smaller cylinder, found out the moment of inertia of outer cylinder and inner cylinder individually. In this question we will not use the value of moment of inertia of a cylinder around its central diameter i.e. .
Complete step-by-step answer:
Here we are given a hollow cylinder with a mass
So the total area of cross section of the cylinder is
Area
The mass
So the mass per unit cross section area is
In this problem we have a hollow cylinder, let’s divide it into two parts: a bigger cylinder with a radius
The mass of the outer cylinder is
Similarly the mass of inner cylinder is
The moment of inertia of the outer cylinder is
The moment of inertia of the inner cylinder is
The net moment of inertia is the difference in the moment of inertia of the outer cylinder and the movement of inertia of the inner cylinder
Hence, option B is the correct choice.
Note: In this problem we divided the hollow cylinder into an outer bigger cylinder and smaller cylinder, found out the moment of inertia of outer cylinder and inner cylinder individually. In this question we will not use the value of moment of inertia of a cylinder around its central diameter i.e.
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