A rod is rotating about an axis passing through its centre and perpendicular to its length. The radius of gyration for the rod is

Question

A rod is rotating about an axis passing through its centre and perpendicular to its length. The radius of gyration for the rod is (A) L / 12 (B) L / √12 (C) L / 6 (D) L / √6

Tardigrade Admin · Accepted Answer

As, moment of inertia of rod, I text rod =(M L2/12) ...(i) Using radius of gyration, I=M k2 ...(ii) Comparing Eqs. (i) and (ii), we get Radius of gyration, k=L / √12

Q. A rod is rotating about an axis passing through its centre and perpendicular to its length. The radius of gyration for the rod is

$L /12$

$L / 12$

$L /6$

$L / 6$

As, moment of inertia of rod,
$I_{rod} = \frac{M L ^{2}}{12}$ ...(i)
Using radius of gyration, $I = M k^{2}$ ...(ii)
Comparing Eqs. (i) and (ii), we get
Radius of gyration, $k = L / 12$

Q. A rod is rotating about an axis passing through its centre and perpendicular to its length. The radius of gyration for the rod is

L/12

L/12​

L/6

L/6​

As, moment of inertia of rod, I rod ​=12ML2​ ...(i) Using radius of gyration, I=Mk2 ...(ii) Comparing Eqs. (i) and (ii), we get Radius of gyration, k=L/12​

$L /12$

$L / 12$

$L /6$

$L / 6$

As, moment of inertia of rod,
$I_{rod} = \frac{M L ^{2}}{12}$ ...(i)
Using radius of gyration, $I = M k^{2}$ ...(ii)
Comparing Eqs. (i) and (ii), we get
Radius of gyration, $k = L / 12$