If rotation of the earth stopped suddenly then the rise in...

If rotation of the earth stopped suddenly then the rise in temperature of the earth, assume total rotational energy is converted into thermal energy, is: (specific heat of earth $=0.15$, radius of earth $=6400 \mathrm{~km}$ ) (a) $78.76^{\circ} \mathrm{C}$ (b) $6.876^{\circ} \mathrm{C}$ (c) $68.76^{\circ} \mathrm{C}$ (d) $0.6876^{\circ} \mathrm{C}$

If rotation of the earth stopped suddenly then the rise in temperature of the earth, assume total rotational energy is converted into thermal energy, is: (specific heat of earth $=0.15$, radius of earth $=6400 \mathrm{~km}$ )
(a) $78.76^{\circ} \mathrm{C}$
(b) $6.876^{\circ} \mathrm{C}$
(c) $68.76^{\circ} \mathrm{C}$
(d) $0.6876^{\circ} \mathrm{C}$

Key Concepts

Rotational Kinetic Energy

Rotational kinetic energy is the energy possessed by a rotating body due to its motion. It is determined by the body’s moment of inertia and angular velocity, and represents the energy stored in the rotation which can be converted into other forms, such as thermal energy under certain conditions.

Moment of Inertia

The moment of inertia quantifies how the mass of an object is distributed relative to the axis about which it rotates. It plays a crucial role in determining the rotational kinetic energy and is dependent on the shape and mass distribution of the object.

Energy Conversion

Energy conversion refers to the process of changing energy from one form to another. In scenarios where the rotational energy of a system is fully converted into thermal energy, the conservation of energy is applied to account for the resultant temperature change.

Specific Heat Capacity

Specific heat capacity is a property of a material that indicates the amount of energy required to raise the temperature of a unit mass of the substance by one degree. It is a key factor when calculating temperature changes resulting from energy inputs such as converted kinetic energy.

Conservation of Energy

The conservation of energy principle states that energy cannot be created or destroyed, only transformed from one form to another. This fundamental concept is critical in analyzing systems where mechanical energy, like rotational kinetic energy, is converted into heat, leading to a change in temperature.

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