Question

iv) 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) 15
(B) 2.5
(C) 22.5
(D) V12.5​

Answer 1

Answer:

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rohitsharma10764

rohitsharma10764

04.05.2020

Physics

Secondary School

+5 pts

Answered

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

1

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Given:

The radius of gyration of a uniform disc about its central and transverse axis =2.5 units

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 :

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

Let , K = radius of gyration

∴

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

Now by theorem of perpendicular axis :

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

∴For a uniform disc ,

So,

Now by theorem of parallel axis :

Moment of inertia about tangent =

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

So, K' =

Since units

So,

= units

Hence , (D) is the correct option i.e. radius of gyration about a tangent of the disc is units .