Question

If the radius of a solid sphere is 35 cm. The radius of gyration when the axis along a tangent is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Moment of inertia of a solid sphere about its tangent,

\(I^1 = I_0 + MR^2 [where I_0 = Moment of inertia about natural axis]

$\Rightarrow I^1=\frac{2}{5}M{R}^2+M{R}^2=\frac{7}{2}M{R}^2$

$\therefore I^1=\frac{7}{5}M{R}^2=M{K}^2$ [where K = Radius of gyration]

$\Rightarrow K=\sqrt[r]{r\frac{7}{5}}=\left(35cm\right)\sqrt{\frac{7}{5}}=7\sqrt{35}cm$