Question

A boiled egg and a raw egg of the same mass and size are made to rotate about their own axis. If $I_1$ and $I_2$ are moments of inertia of boiled egg and raw egg respectively, then:
A) I₁=I₂
B) I₁>I₂
C) I₁< I₂
D) I₁=√2I₂

Answer 1

Hint: When angular momentum is the same, it is indirectly proportional to ω.

Complete step by step solution:
Boiled egg rolls slower than a raw egg, because it has a higher moment of inertia than a raw egg. In order to conserve angular momentum, the angular velocity of the boiled egg decreases.
The hard-boiled egg moves as if it was one solid unit. The raw egg has a solid shell but various types of fluids inside that can move independently of the shell. When you turn the egg to cause it to spin this rotating or turning force is called a torque.
The rotating force on the shell of the hard-boiled egg spins the entire egg –shell and content because the content is solid and moves when the shell moves. This egg easily spins and spins longer than does the raw egg.

Thus, moments of inertia of boiled egg(I₁) lesser than moments of inertia of raw egg(I₂)

Correct answer: C) I₁< I₂

Note: Mass in case of boiled egg is concentrated near the axis of rotation and mass of raw egg is concentrated at the surface away from the axis of rotation.