The radius of gyration of an uniform rod of length l about an axis passing through one of its ends and perpendicular to its length is

Question

The radius of gyration of an uniform rod of length l about an axis passing through one of its ends and perpendicular to its length is (A) (l/√2) (B) (l/3) (C) (l/√ 3) (D) (l/2)

Tardigrade Admin · Accepted Answer

Moment of inertia of rod of mass M and length l about its axis passing through one of its ends and perpendicular to it is I = (1/3) Ml2 As I = Mk2 where k is the radius of the gyration ∴ Mk2 = (1/3)Ml2 or k = (l/√ 3)

Q. The radius of gyration of an uniform rod of length $l$ about an axis passing through one of its ends and perpendicular to its length is

$\frac{l}{2}$

$\frac{l}{3}$

$\frac{l}{3}$

$\frac{l}{2}$

Moment of inertia of rod of mass $M$ and length $l$ about its axis passing through one of its ends and perpendicular to it is
$I = \frac{1}{3} M l^{2}$
As $I = M k^{2}$ where $k$ is the radius of the gyration
$∴ M k^{2} = \frac{1}{3} M l^{2}$ or $k = \frac{l}{3}$

Q. The radius of gyration of an uniform rod of length l about an axis passing through one of its ends and perpendicular to its length is

2​l​

3l​

3​l​

2l​

Moment of inertia of rod of mass M and length l about its axis passing through one of its ends and perpendicular to it is I=31​Ml2 As I=Mk2 where k is the radius of the gyration ∴Mk2=31​Ml2 or k=3​l​

Q. The radius of gyration of an uniform rod of length $l$ about an axis passing through one of its ends and perpendicular to its length is

$\frac{l}{2}$

$\frac{l}{3}$

$\frac{l}{3}$

$\frac{l}{2}$

Moment of inertia of rod of mass $M$ and length $l$ about its axis passing through one of its ends and perpendicular to it is
$I = \frac{1}{3} M l^{2}$
As $I = M k^{2}$ where $k$ is the radius of the gyration
$∴ M k^{2} = \frac{1}{3} M l^{2}$ or $k = \frac{l}{3}$