Q3 done in similar way as this
Particles of masses 1g,2g,3g,............100g are kept at the marks 1cm,2cm,3cm...........100cm respectively on a metre scale.Find the moment of inertia of the system of particles about a perpendicular bisector of the metre scale.
Sol:moment of inertia abt perpendicular bisector
= m1 r1^2 + m2r2^2 + m3r3^2 + .....
=1 * 49^2 + 2 * 48^2 +.....49*1^2 + 50*0^2 + 51*1^2 + .............99*49^2 + 100 * 50^2
combining the first and the second last, second and the third last , .....
we get
MI=100 * 50^2 + (1+99) * 49^2 +............(49+51)*1^2
=100(50^2 + 49^2 +.........1^2)
=100 n(n+1)(2n+1) / 6 where n= 50
=100 *50*51*101 / 6
=4292500 g cm^2
=0.42925 kg m^2