Question

Four masses are joined to a light circular frame as shown in the figure. The radius of
gyration of this system about an axis passing through the centre of the circular frame and
perpendicular to its plane would be
(a) a/√2
(b) a/2
(c) a
(d) 2a​

Answer 1

Answer:

2a

Explanation:

this is your answer please check it out

Answer 2

answer : option (c) a

explanation : The radius of gyration is given by, $k=\sqrt{\frac{I}{M}}$

where I is moment of inertia about an axis and M is total mass of system of bodies.

here, total mass, M = 2m + 3m + 2m + m = 8m

moment of inertia about an axis passing through AA' , I = 2ma² + 3ma² + 2ma² + ma² = 8ma²

so, k = $\sqrt{\frac{8ma^2}{8m}}$

= a

hence, radius of gyration of this system about an axis passing through the centre of the circular frame and

radius of gyration of this system about an axis passing through the centre of the circular frame andperpendicular to its plane would be a