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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) respectively. Find the moment of inertia of the system of particles (in g-cm2) about z axis.

A
48 g-cm2
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B
96 g-cm2
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C
108 g-cm2
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D
176 g-cm2
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Solution

## The correct option is C 108 g-cm2Given: m1=1 g,m2=2 g,m3=3 g,m4=4 g Co-ordinates of mass m1(x1,y1)=(0 cm,0 cm) Co-ordinates of mass m2(x2,y2)=(0,3 cm) Co-ordinates of mass m3(x3,y3)=(3 cm,3 cm) Co-ordinates of mass m4(x4,y4)=(3 cm,0) Therefore, moment of inertia of the system about z− axis I=m1r21+m2r22+m3r23+m4r24 (where r1,r2,r3 and r4 are perpendicular distances from z-axis) From diagram, r1=0 cm,r2=3 cm,r3=3√2 cm,r4=3 cm ⇒I=1(0)2+2(3)2+3(3√2)2+4(3)2 =108 g-cm2

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