91影视

table 9.2 gives,

\(I = \frac{2}{3}M{R^2}\)

We know that in a solid sphere with mass M and,

Radius =R

Along a diameter\({I_{cm}} = \frac{2}{5}M{R^2}\).

Now here we need to find the diameter,

We use the parallel axis theorem.

\({I_p} = {I_{cm}} + M{d^2}\)

we know that \({I_{cm}} = \frac{2}{5}M{R^2}\) and \({I_p} = \frac{2}{3}MR{}^2\).

\({I_p} = {I_{cm}} + M{d^2}\)

Put the value in the given expression,

\(\frac{2}{5}M{R^2} = \frac{2}{3}MR{}^2 + M{d^2}\)

\(\frac{2}{5}M{R^2} - \frac{2}{3}MR{}^2 = M{d^2}\)

\(M{R^2}\left( {\frac{2}{5} - \frac{2}{3}} \right) = M{d^2}\)

\({R^2}\left( {\frac{2}{5} - \frac{2}{3}} \right) = {d^2}\)

\(d = \sqrt {{R^2}\left( {\frac{2}{5} - \frac{2}{3}} \right)} \)

\( = \sqrt {{R^2}\left( {\frac{{10 - 6}}{{15}}} \right)} \)

\( = \sqrt {\frac{4}{{15}}} R\)

\( = \frac{2}{{\sqrt {15} }}R\)

\(d = 0.516R\)

Hence, the axis is parallel to the diameter \(0.516R\)from the center.