A composite body consists of a solid cylinder and a solid sphere, both of mass M and radius R. What is the total moment of inertia about the same axis?
Practice Questions
1 question
Q1
A composite body consists of a solid cylinder and a solid sphere, both of mass M and radius R. What is the total moment of inertia about the same axis?
(7/10) MR^2
(9/10) MR^2
(11/10) MR^2
(13/10) MR^2
The total moment of inertia is I_cylinder + I_sphere = (1/2 MR^2) + (2/5 MR^2) = (7/10) MR^2.
Questions & Step-by-step Solutions
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Q
Q: A composite body consists of a solid cylinder and a solid sphere, both of mass M and radius R. What is the total moment of inertia about the same axis?
Solution: The total moment of inertia is I_cylinder + I_sphere = (1/2 MR^2) + (2/5 MR^2) = (7/10) MR^2.
Steps: 10
Step 1: Identify the shapes involved in the composite body. We have a solid cylinder and a solid sphere.
Step 2: Note the mass (M) and radius (R) of both the cylinder and the sphere.
Step 3: Find the moment of inertia formula for the solid cylinder. It is I_cylinder = (1/2) * M * R^2.
Step 4: Find the moment of inertia formula for the solid sphere. It is I_sphere = (2/5) * M * R^2.
Step 5: Add the moments of inertia of the cylinder and the sphere together: I_total = I_cylinder + I_sphere.
Step 6: Substitute the formulas into the equation: I_total = (1/2) * M * R^2 + (2/5) * M * R^2.
Step 7: To add the fractions, find a common denominator. The common denominator for 2 and 5 is 10.
Step 8: Rewrite the fractions: (1/2) = (5/10) and (2/5) = (4/10).
Step 9: Now add the fractions: I_total = (5/10) * M * R^2 + (4/10) * M * R^2 = (9/10) * M * R^2.
Step 10: Therefore, the total moment of inertia about the same axis is (9/10) * M * R^2.
