Rotational Mechanics
Classical Mechanics
Level
2
Particles of mass 1 g, 2 g,3 g,...,100 gare kept at the marks 1 cm,2 cm,3 cm,....,100 cm respectively on a metre scale. Find the moment of inertia of a system of particles about a perpendicular bisector on the metre scale.(in kg m^2)
The answer is 0.43.
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1 solution
The perpendicular bisector is at x=50 cm. Now take a a pair of masses at a distance of 1cm i.e, from x=50cm, take the masses at x=49 cm and x=48cm respectively and add their moments of inertia. Now take another pair at distance 2cm from x=50cm. Now add their moments of inertia as well. By adding these, we can observe that the moment of inertia of whole system about x=50cm comes out to be 100 x (sum of squares of natural numbers from n=1 to n=50) which can be calculated and then converted into kgm^2 by considering proper units