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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-cm2Given: 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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