Question

In a certain unit, the radius of gyration

of a uniform disc about its central and

transverse axis is 2 5. . Its radius of

gyration about a tangent in its plane (in

the same unit) must be
(A) √5 (B) 2.5

(C) 2 √2.5(D) √12.5​

Answer 1

Given:

Radius of gyration of a uniform disc = 2.5

To Find:

Radius of gyration about tangent in its plane

Solution:

Moment of Inertia of disc about center of mass is I =  mr²/2

Let a line parallel to x axis = d

Radius of a gyration = r

Thus, mR²/2 = mR²

= R² = R²/r

= R = R/√2

Now R/√2 = 2.5 (Given)

By theorum of perpendicular axis - Ix + Iy = Iz

where Ix, Iy and Iz are moment of inertia about x, y and z axis

Thus,  

Ix = Iy = mR²/ 2 × 2 = mR²/4

mR²/4 + mR² = 5mR²/4

Let the tangent be = T

mT = 5mr/4

t = 5R²/2

Since r/√2 = 2.4

T = √5/√2 × 2.5

= √12.5

 Answer: The radius of gyration is (D) √12.5​

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