Question

Four identical particles (mass of each = 0.24 kg) are placed at the vertices of a rectangle (2.0 m × 3.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the moment of inertia of this rigid body about an axis that passes through the center of mass of the body and is parallel to the shorter sides of the rectangle?

Answer 1

Answer:

2.16 kgm²

Explanation:

Width = 3 m

According to the question distance would be

$r=\dfrac{Width}{2}\\\Rightarrow r=\dfrac{3}{2}\\\Rightarrow r=1.5\ m$

Moment of inertia is given by

$I=mr^2\\\Rightarrow I=0.24\times 1.5^2\\\Rightarrow I=0.54\ kgm^2$

Moment of inertia of system from the center of mass

$I_s=4I\\\Rightarrow I_s=4\times 0.54\\\Rightarrow I_s=2.16\ kgm^2$

The moment of inertia of this rigid body about an axis that passes through the center of mass of the body and is parallel to the shorter sides of the rectangle is 2.16 kgm²