Question:
The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is
The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is
Updated On: Apr 25, 2024
- 2:1
- \(\sqrt2:1\)
- 4:1
- \(1:\sqrt2\)
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The Correct Option is B
Solution and Explanation
\(I_1 = \frac{MR_2}{2} = MK_{12}\)
\(I_2 = \frac{MR_2}{4} = MK_{22}\)
\(K_1 = \frac{R}{\sqrt2}, K_2 = \frac{R}{2}\)
\(\frac{K_1}{K_2} = (\frac{1}{√2})(\frac{2}{1}) = \frac{2}{1}\)
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.