Question

Three particles, each of mass 0.5 kg, are situated at the

corners of an equilateral triangle if side 0.4 m. Find the

M.I. and radius of gyration of the system about an axis

passing through the centroid of the triangle and

perpendicular to its plane.

Answer 1

distance of each corner from the centroid of the triangle is given by

$r = \frac{a}{\sqrt3}$

given that a = 0.4 m

$r = 0.23 m$

now by the formula of moment of inertia

$I = 3*mr^2$

given that

m = 0.5 kg

now plug in all values

$I = 3*0.5*0.23^2$

$I = 0.08 kg m^2$

now we will have to find radius of gyration which is defined as

$k =\sqrt{\frac{I}{3m}}$

$k =\sqrt{\frac{0.08}{3*0.5}}$

$k = 0.23 m$

so radius of gyration is same as centroid radius