The incorrect statement among the given options is option 'D': The Earth's core has a radius of 1500 km.

Explanation:

The Earth is composed of several layers, including the crust, mantle, outer core, and inner core. Each layer has distinct properties and characteristics. Let's discuss each of the given options in detail:

a) S wave cannot be sent through a liquid medium:
- S waves, also known as shear waves, are a type of seismic wave that travels through the Earth's interior during an earthquake.
- These waves can only pass through solid materials and cannot propagate through liquids.
- This is because liquids do not possess shear strength, which is required for the transmission of S waves.
- Therefore, statement a) is correct.

b) The mantle consists of solid rock:
- The mantle is a layer located between the Earth's crust and outer core.
- It is predominantly composed of solid rock, specifically silicate minerals, including pyroxenes, olivines, and garnets.
- The solid-state of the mantle allows for the transmission of both P waves (primary waves) and S waves during seismic events.
- Therefore, statement b) is correct.

c) S wave terminates at the mantle-core boundary:
- The mantle-core boundary is the boundary between the Earth's mantle and outer core.
- S waves can propagate through the mantle but cannot pass through the outer core.
- This is because the outer core is composed mainly of liquid iron and nickel, lacking the necessary shear strength for S wave transmission.
- Therefore, statement c) is correct.

d) The Earth's core has a radius of 1500 km:
- The Earth's core is divided into two parts: the outer core and the inner core.
- The outer core is a liquid layer composed mainly of molten iron and nickel.
- The inner core, however, is solid and primarily consists of solid iron and nickel.
- The radius of the Earth's core is approximately 3486 km, not 1500 km.
- Therefore, statement d) is incorrect.

In conclusion, the incorrect statement is d) The Earth's core has a radius of 1500 km. The correct radius of the Earth's core is approximately 3486 km.