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Two identical spheres fixed at the ends of a light rod: moment of inertia about the perpendicular axis through the centre

The same question, asked 3 times: 2021 Paper 23*, 6 Apr 2023*, 31 Jan 2024. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 23

    3
    A system consists of two identical spheres each of mass 1.5 kg1.5\text{ }kg and radius 50 cm50\text{ }cm at the end of light rod. The distance between the centres of the two spheres is 5 m5\text{ }m. What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its midpoint?

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  2. Question 2

    6 Apr 2023

    29
    Two identical solid spheres each of mass 2 kg2\text{ }kg and radii 10 cm10\text{ }cm are fixed at the ends of a light rod. The separation between the centres of the spheres is 40 cm40\text{ }cm. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is ___×10−3 kg−m2\_\_\_\times10^{- 3}\text{ }kg -m^{2}

  3. Question 3

    31 Jan 2024

    118
    Two identical spheres each of mass 2 kg2\text{ }kg and radius 50 cm50\text{ }cm are fixed at the ends of a light rod so that the separation between the centers is 50 cm50\text{ }cm. Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is x20 kg m2\frac{x}{20}\text{ }kg{\text{ }m}^{2}, where the value of xx is_____