Question:medium

If the moment of inertia of a body along a perpendicular axis passing through its centre of gravity is 50 kg.m2 and the mass of the body is 30 kg. What will be the moment of inertia (kg.m2) of the same body along another axis, which is 50 cm away from the current axis and parallel to it?

Show Hint

Use the parallel axis theorem, and be careful to convert 50 cm into metres before squaring it.
  • 80.0
  • 57.5
  • 110.0
  • 65.0
Show Solution

The Correct Option is B

Solution and Explanation

The parallel axis theorem simply says that moving your axis away from the centre of gravity always increases the moment of inertia, by an amount equal to the mass times the square of the shift distance.

Here the shift distance is \(d = 50\ cm = 0.5\ m\), and the mass is \(m = 30\ kg\). So the extra term added to the centroidal value is \(m d^2 = 30 \times 0.25 = 7.5\ kg.m^2\).

Starting from the centroidal moment of inertia of \(50\ kg.m^2\), the new moment of inertia about the shifted parallel axis is \(50 + 7.5 = 57.5\ kg.m^2\).

\[\boxed{I = 57.5\ kg.m^2}\]
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