Two solid spheres of masses 5 kg and 10 kg with radii 10 cm and 20 cm respectively are kept in contact. Find the moment of inertia of the system about the common tangent.

For a solid sphere:

I_cm = 2/5 MR²

Using parallel axis theorem:

First sphere

Mass = 5 kg
Radius = 0.1 m

I₁ = (2/5)(5)(0.1)² + 5(0.1)²

= 0.02 + 0.05

= 0.07 kg m²

Second sphere

Mass = 10 kg
Radius = 0.2 m

I₂ = (2/5)(10)(0.2)² + 10(0.2)²

= 0.16 + 0.40

= 0.56 kg m²

Total moment of inertia:

I = I₁ + I₂

= 0.07 + 0.56

= 0.63 kg m²

Answer:

0.63 kg m²