Question

four bodies of mass 2kg 3kg 4kg and 5kg are placed at points A BC andD of a square ABCD of side 1m.The radius of gyration of the system about an axis passing through A and perpendicular toits plane is​

Answer 1

★ Distance between A and B = 1 m (along the side).

★ Distance between A and C = √(1² + 1²) = √2 m (along the diagonal).

★ Distance between A and D = 1 m (along the side).

Hence,

$\displaystyle\longrightarrow\sf {I=MK^2}$

$\displaystyle\longrightarrow\sf {2(0)^2+3(1)^2+4(\sqrt2)^2+5(1)^2=(2+3+4+5)K^2}$

$\displaystyle\longrightarrow\sf {16=14K^2}$

$\displaystyle\longrightarrow\sf {\underline {\underline {K=\sqrt{\dfrac {8}{7}}\ m}}}$

$\displaystyle\longrightarrow\sf {\underline {\underline {K=1.07\ m}}}$