Question

Find (1) radius of gyration (2) M.I of a rod of mass 100g & length 100 cm about an axis passing through its centre & to its length.

Answer 1

Given,

Mass of rod, $M=0.1kg$
Length of rod, $L=0.1m$

Radius of gyration at center, $K_c=\frac{L^2}{12}=\frac{{0.1}^2}{12}=8.3\times {10}^{-4}{m}^2$

Radius of gyration at length's end, $K_e=\frac{L^2}{3}=\frac{{0.1}^2}{3}=3.3\times {10}^{-3}{m}^2$

Moment of inertia at center, $I_c=\frac{M{L}^2}{12}=\frac{0.1\times {0.1}^2}{12}=8.3\times {10}^{-5}kg{m}^2$

Moment of inertia at length's end, $I_e=\frac{M{L}^2}{3}=\frac{0.1\times {0.1}^2}{3}=3.3\times {10}^{-4}kg{m}^2$