Final answer:
If the planet's core cools down, it will result in a slower flow of hot rock in Earth's mantle.
Step-by-step explanation:
If the planet's core eventually cools down, it will have an impact on the flow of hot rock in Earth's mantle. The core is responsible for generating heat in the mantle through nuclear reactions. This heat causes convection currents in the mantle, where warmer material rises and cooler material sinks. As the core cools down, the heat input decreases, leading to a decrease in the temperature difference between the upwelling and sinking material. This will result in a slower flow of hot rock in the mantle.