1. **Problem Statement:** A child whirls a toy tied to a string in a horizontal circle of radius $R$ with a period $T$. Find the magnitude of the acceleration of the toy. 2. **Formula and Explanation:** The toy moves in uniform circular motion, so it experiences centripetal acceleration directed towards the center of the circle. The magnitude of centripetal acceleration is given by: $$a = \frac{v^2}{R}$$ where $v$ is the linear speed of the toy. 3. **Relating speed to period:** The toy completes one revolution in time $T$, so the circumference of the circle is $2\pi R$, and the speed is: $$v = \frac{2\pi R}{T}$$ 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, it depends on $R$ and $T$ as shown. **Final answer:** The magnitude of the acceleration is $$\boxed{\frac{4\pi^2 R}{T^2}}$$ which corresponds to option B.