1. Given: A ball is dropped from rest from the top of a tower of height $h$.

2. Use equation of motion for free fall: Since the ball is released from rest, $s = \frac{1}{2}gt^2$ where $s$ is the distance fallen in time $t$.

3. At time $T$, the ball reaches the ground, so the total distance fallen is $h$: $h = \frac{1}{2}gT^2$

4. At time $\dfrac{T}{3}$, the distance fallen is: $s' = \frac{1}{2}g\left(\frac{T}{3}\right)^2$ $s' = \frac{1}{2}g\cdot \frac{T^2}{9}$ $s' = \frac{1}{9}\left(\frac{1}{2}gT^2\right)$

5. From step 3, $\frac{1}{2}gT^2 = h$, so: $s' = \frac{h}{9}$

6. This is the distance fallen from the top. Therefore, the height of the ball from the ground after $\dfrac{T}{3}$ seconds is: $h - \frac{h}{9} = \frac{8h}{9}$

7. Check options:

   • A: $\dfrac{8h}{9}$ from the ground ✅
   • B: $\dfrac{7h}{9}$ from the ground ❌
   • C: $\dfrac{h}{9}$ from the ground ❌ (this is distance fallen, not distance from ground)
   • D: $\dfrac{7h}{18}$ from the ground ❌

Therefore, the correct answer is A.