1. Physical condition for proper mixing

If the drum rotates too fast, the concrete sticks to the wall and does not fall down.

For proper mixing, the material should just not remain stuck to the wall at the topmost point.

So, the maximum allowed speed is the speed at which the mixture is just about to lose contact at the top.

At the topmost point, the required centripetal force is provided by:

• weight $mg$
• normal reaction $N$

For the limiting case of just maintaining contact, $N=0$ so, $mg = \frac{mv^2}{r}$

Thus, $v = \sqrt{gr}$

2. Relate linear speed to angular speed

Since $v = \omega r$ we get $\omega = \sqrt{\frac{g}{r}}$

Given: $r=1.25\,\text{m}, \quad g\approx 9.8\,\text{m/s}^2$

So, $\omega = \sqrt{\frac{9.8}{1.25}} = \sqrt{7.84} = 2.8\,\text{rad/s}$

3. Convert angular speed to revolutions per minute

Frequency in revolutions per second is $f = \frac{\omega}{2\pi} = \frac{2.8}{2\pi}$

Using $2\pi \approx 6.283$, $f \approx \frac{2.8}{6.283} \approx 0.446\,\text{rev/s}$

Therefore, in rpm: $\text{rpm} = 0.446 \times 60 \approx 26.8$

So the maximum rotational speed is close to $27\,\text{rpm}$

4. Check options

• A: $0.4$ rpm — too small
• B: $1.3$ rpm — too small
• C: $8.0$ rpm — too small
• D: $27.0$ rpm — correct

Hence, the correct option is D.