1. **State the problem:** We have a two-wheel system where wheel 1 rotates at 200 rpm with radius 21 cm and torque 3000 NM. Wheel 2 rotates at 1000 rpm. We need to find the radius of wheel 2. 2. **Relevant formula:** In a two-wheel system connected by a belt or chain, the linear speed at the rim of both wheels is the same. The linear speed $v$ is related to angular speed $\omega$ and radius $r$ by: $$v = r \times \omega$$ Since the wheels are connected, their linear speeds are equal: $$r_1 \times \omega_1 = r_2 \times \omega_2$$ 3. **Convert rpm to angular velocity:** Angular velocity in radians per minute is proportional to rpm, so we can use rpm directly since it cancels out. 4. **Solve for $r_2$:** $$r_2 = \frac{r_1 \times \omega_1}{\omega_2}$$ Substitute values: $$r_2 = \frac{21 \times 200}{1000}$$ 5. **Simplify:** $$r_2 = \frac{21 \times \cancel{200}}{\cancel{1000}} = \frac{4200}{1000} = 4.2$$ 6. **Final answer:** The radius of wheel 2 is **4.2 cm**.