1. **Problem statement:** A child whirls a toy tied to a string in a horizontal circle of radius $R$ with period $T$. Find the magnitude of the acceleration of the toy. 2. **Formula used:** The acceleration of an object moving in uniform circular motion is the centripetal acceleration given by $$a = \frac{v^2}{R}$$ where $v$ is the speed of the object. 3. **Relate speed to period:** The speed $v$ is the circumference divided by the period: $$v = \frac{2\pi R}{T}$$ 4. **Substitute $v$ into acceleration formula:** $$a = \frac{\left(\frac{2\pi R}{T}\right)^2}{R} = \frac{4\pi^2 R^2}{T^2 R} = \frac{4\pi^2 R}{T^2}$$ 5. **Interpretation:** The acceleration is not zero, and it depends on $R$ and $T$ as shown. **Final answer:** The magnitude of the acceleration is $$a = \frac{4\pi^2 R}{T^2}$$ which corresponds to option B.