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Question

What is the dimensional formula for the radius of gyration?


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Solution

Step 1: Definition

  1. The radius of gyration is defined as the imaginary distance from the centroid at which the area of cross-section is imagined to be focused at a point in order to obtain the same moment of inertia.
  2. The radius of gyration is denoted by K.
  3. Formula: K=Im. Here, I is the moment of inertia, m is the mass.

Step 2: Dimensional formula for the radius of gyration

We know

Dimensional formula of Mass =[M1L0T0]

Dimensional formula of Moment of Inertia =[M1L2T0]

Putting these values in the formula of the radius of gyration, we get

Dimensional formula of the radius of gyration =[M1L2T0][M1L0T0]

=[M0L1T0]

Therefore, the dimensional formula of the radius of gyration is [M0L1T0].


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