Question

The position of axis of rotation of a body is changed so that its moment of inertia decreases by 36%. Find the % change in its radius of gyration.

• A. It decreases by 18%
• B. It increases by 18%
• C. It decreases by 20%
• D. It increases by 20%

Answer 1

Answer: (C)

We know that $I=M{K}^2$

Where, $I=$ moment of inertia, $M=$ mass of body, $K=$radius of gyration.

Therefore, $K=\sqrt{\frac{I}{M}}$

Let the initial MOI be $100I_1$ so $K_1=10I_1$

Now the MOI will be decreased by $36$

So, final MOI after change will be $I_2=\frac{100I_1-36I_1}{100I_1}\times 100$ so $K_2=8I_1$

So, change in radius of gyration will be $\Delta K=\frac{K_1-K_2}{K_1}=\frac{{10}_{I_1}-8_{I_1}}{{10}_{I_1}}\times 100=20$