Question

show that k²/R² = 2/5 for the uniform solid sphere where K is radius of gyration and R is radius of sphere.​

Answer 1

Answer:

☆Definitions:

•Radius of gyration:

=> it defines,that if we totally condensed the continuous mass body into particle mass then, by placing it at some distance 'k' it will give the same moment of inertia as it gives as continuous body.

$\boxed{\bf{ I = mk^{2}}}$

(where I is the moment of inertia)

☆Solution:

》I of solid sphere = $\frac {2}{5}$m$\R^{2}$

》m$\ k^{2}$ = $\frac {2}{5}$m$\R^{2}$

》$\ k^{2}$ = $\frac {2}{5}$$\R^{2}$

》$\frac {k^{2}}{R^{2}}$ = $\frac {2}{5}$

Henced proved!

♧hope it helps!♧