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The moment of inertia of a uniform rod of mass .50 kg and length 1 m is .10kgm2 about a line perpendicular to the rod. Find the distance of this line from the middle point of the rod.plz explain the ans.

The moment of inertia of a uniform rod of mass .50 kg and length 1 m is .10kgm2 about a line perpendicular to the rod. Find the distance of this line from the middle point of the rod.plz explain  the ans.

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1 Answers

Arun
25750 Points
5 years ago
Given in the question,
Length of the Rod - 1 m
Mass of the Rod - 0.5 g

Moment of Inertia at perpendicular bisector

I = ml^2 / 12

=0.50 × 1² /12
=1/ 24 kg.m

At the distance r the moment of inertia , rod middle point l' = 0.10 kg-m²

I’ = I + m r^2
0.10 = 1/ 24 +0.50 r²
1+0.50× 24 r² =0.10× 24
12 r² =2.4 -1
r² =1.4/12 
r²=0.467/4
r= 0.68/2
r= 0.34 m.

Hence the distance from the middle point is equal to 0.34 m.

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