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Question
The moment of inertia of a uniform rod of mass 0⋅50 kg and length 1 m is 0⋅10 kg-m2about a line perpendicular to the rod. Find the distance of this line from the middle point of the rod.
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Solution
Given
Length of the rod, l = 1 m
Mass of the rod, m = 0.5 kg
Let the rod moves at a distance d from the centre.
On applying parallel axis theorem, we get
Moment of inertia about that axis,
\[I = \left( \frac{m l^2}{12} \right) + m d^2 = 0 . 10\]
\[I = \frac{0 . 5 \times l^2}{12} + 0 . 5 \times d^2 = 0 . 10\]
\[ \Rightarrow \frac{1}{12} + d^2 = 0 . 2\]
\[ \Rightarrow d^2 = 0 . 118\]
\[ \Rightarrow d = 0 . 342\text{ m from the centre}\]
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