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

Answer:

To Find :

The radius of gyration of the uniform disc about a tangent in its plane = ?

Solution :

Since we know that the moment of inertia disc about central transverse axis is given as :

= $\frac{mR^2}{2}}$

Here m and R are mass and radius of disc respectively .

Let , K = radius of gyration

∴ ${mK^2\:= \frac{mR^2}{2}}$

So,$K = \frac{R}{\sqrt[2]{2}}$

= 2.5 units (radius of gyration is given 2.5 units )

Now by theorem of perpendicular axis :

Ix + Iy = Iz

Where Ix , Iy and Iz are the moment of inertia about x , y and z axis .

∴For a uniform disc , Ix = II

So, Ix = Iy =$\frac{mR^2}{2\times 2}$

$= \frac{mR^2}{4}$

Now by theorem of parallel axis :

Moment of inertia about tangent =

${\frac{mR^2}{4} \:+\:{mR^2}}$

$= \frac{5mR^2}{4}$

Let K' be the radius of gyration about the tangent , then :

mK'² = $\frac{5mR^2}{4}$

So, K' = $\frac{\sqrt[5]{R}}{2}$

Since $\frac{R}{\sqrt[2]{2}}$

=2.5 units

So, K' = ${\frac{\sqrt[2]{5}}{\sqrt[2]{2}}\:×\:2.5}$

= √12.5 units

Hence , radius of gyration about a tangent of the disc is

= √12.5 units

Answer 2

Answer:

Refers to the attachment