Four masses are joined to a light circular frame as shown in the figure. The rad

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

Options:

A . a√2

B . a2

C . a

D . 2a

Answer: Option C
:
C
Since the circular frame is massless so we will consider moment of inertia of four masses only.

I = m a^{2} + 2 m a^{2} + 3 m a^{2} + 2 m a^{2} = 8 m a^{2}

.....(i)
Now from the definition of radius of gyration

I = 8 m k^{2}

.....(ii)
comparing (i) and (ii) radius of gyration k = a.

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