Question

Four masses are joined to a light circular frame as shown in the figure. The radius of gyration of this system about the axis $A{A}^{\prime }$is.

• A. $\frac{a}{\sqrt{2}}$
• B. $\frac{a}{2}$
• C. $a$
• D. $2a$

Answer 1

The correct option is C $a$

Since the circular frame is massless so we will consider moment of inertia of four masses only.
$I=m{a}^2+2m{a}^2+3m{a}^2+2m{a}^2=8m{a}^2$ .....(i)
Now from the definition of radius of gyration $I=8m{k}^2$ .....(ii)
comparing (i) and (ii) radius of gyration k = a.