A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact i $s_________kg.m².$
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Question

A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact i $s_________kg.m².$

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G1 Physics · Accepted Answer

For a solid sphere, the moment of inertia about any diameter through its centre is I(CM) = (2/5)mR². The required axis is tangent to each sphere at the common point of contact. It is parallel to a diameter through the centre of each sphere and is at distance R from that centre. Using the parallel-axis theorem, I(tangent) = I(CM) + mR² = (2/5)mR² + mR² = (7/5)mR². Therefore, for the two spheres, I(total) = (7/5)[m₁R₁² + m₂R₂²]. Here, m₁ = 5 kg, R₁ = 10 cm = 0.10 m, m₂ = 10 kg, R₂ = 20 cm = 0.20…

A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact i s_________kg.m².