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Question

A thin square plate of side 4 cm and mass m has a moment of inertia ISq about the line AB as shown in figure. It is then reformed into a rectangle of length 8 cm and breadth 2 cm with a moment of inertia IRect about the line CD as shown in the figure. What is the value of the ratio ISqIRect?


  1. 1
  2. 12
  3. 2
  4. 14


Solution

The correct option is A 1
The axis passes through one of the sides of the square
Moment of inertia of square about the axis AB,
IAB=m×a23
a=4 cm=0.04 m
ISq=m×(0.04)23
The axis CD passing through the mid  point of the length of the rectangle with length L=8 cm=0.08 m

IRect=mL212=m×(0.08)212

ISqIRect=m×(0.04)23m×(0.08)212=44=1

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