The moment of inertia of a uniform thin rod about an axis passing through one of its ends and perpen

Question

The moment of inertia of a uniform thin rod about an axis passing through one of its ends and perpendicular to its length is $3600 	ext{ g cm}^2$. If the mass of the rod is $300 	ext{ g}$, its length is exactly

Professor PC Thomas Classes · Answer

(a) : The moment of inertia of a thin rod about an axis passing through its end and perpendicular to its length is given by $I_{end} = \frac{ML^2}{3}$. We are given $I_{end} = 3600 	ext{ g cm}^2$ and $M = 300 	ext{ g}$. Substituting these values into the formula yields: $3600 = \frac{300 	imes L^2}{3} \Rightarrow 3600 = 100 	imes L^2 \Rightarrow L^2 = 36$. Therefore, the length of the rod is $L = 6 	ext{ cm}$.