Three objects are situated at different positions on the x-axis. The first objec

Question

Three objects are situated at different positions on the x-axis. The first object has a mass of 3.5 kg and is at x=2.0m, the second has a mass of 3.6 kg and is at x=9.0 cm, and the third has a mass of 1.2 kg. The axis of rotation passes through the origin perpendicular to the x-axis. What is the magnitude of the distance between the third mass and the origin if the moment of inertia(or the rotational inertia) of the system is 740.0 kg m^2? Three objects are situated at different positions on the x-axis. The first object has a mass of 3.5 kg and is at x=2.0m, the second has a mass of 3.6 kg and is at x=9.0 cm, and the third has a mass of 1.2 kg. The axis of rotation passes through the origin perpendicular to the x-axis. What is the magnitude of the distance between the third mass and the origin if the moment of inertia(or the rotational inertia) of the system is 740.0 kg m^2?

Explanation / Answer

The moment of inertia of the system is the addition of the moment of inertia of the three objects.

Now, moment of inertia of a particular object -

I = MR² where c=1

So as per the condition -  
3.5*2.0² + 3.6*9.0² + 1.2x² = 740
=> 1.2x² = 740 – 14 – 291.6 = 434.4
=> x = sqrt(434.4 / 1.2) = 19.03 m.

So the distance between the third mass and the origin = 19.03 m.

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