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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 dis about its diameter is :  
  • a)
    √2 : 1
  • b)
    4 : 1  
  • c)
    1 : √2
  • d)
    2 : 1 
Correct answer is option 'A'. Can you explain this answer?
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The ratio of the radius of gyration of a thin uniform disc about an axis passing through its center and normal to its plane to the radius of gyration of the disc about its diameter is:

a) 1:√2

The radius of gyration (k) of a thin uniform disc about an axis passing through its center and normal to its plane is given by:

k₁ = (√(mR²/4))/√(m/πR²) = R/2√2

where m is the mass of the disc and R is its radius.

The radius of gyration (k) of the disc about its diameter is given by:

k₂ = (√(mR²/8))/√(m/πR²) = R/√8

The ratio of k₁ to k₂ is:

k₁/k₂ = (R/2√2)/(R/√8) = √8/2√2 = 1/√2 = √2/2

Therefore, the ratio of the radius of gyration of a thin uniform disc about an axis passing through its center and normal to its plane to the radius of gyration of the disc about its diameter is 1:√2.
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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 dis about its diameter is : a)√2 : 1b)4 : 1c)1 : √2d)2 : 1Correct answer is option 'A'. Can you explain this answer?
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