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Question

Four particles of masses 1 g,2 g,3 g and 4 g are kept at points (0,0),(0,3 cm),(3 cm,3 cm),(3 cm,0 cm) respectively. Find the moment of inertia of the system of particles (in g-cm2) about y axis.


A
63 g-cm2
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B
21 g-cm2
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C
10.5 g-cm2
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D
16.67 g-cm2
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Solution

The correct option is A 63 g-cm2
Given:
m1=1 g,m2=2 g,m3=3 g,m4=4 g
Co-ordinates of mass m1(0,0)=(x1,y1)
Co-ordinates of mass m2(0,3 cm)=(x2,y2)
Co-ordinates of mass m3(3 cm,3 cm)=(x3,y3)
Co-ordinates of mass m4(3 cm,0)=(x4,y4)

Therefore, moment of inertia of the system about y axis
I=m1r21+m2r22+m3r23+m4r24
(where r1,r2,r3 and r4 are perpendicular distances from y-axis)

I=m1x21+m2x22+m3x23+m4x24
I=1(0)2+2(0)2+3(3)2+4(3)2
I=63 g-cm2

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