Question

Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is close to : (Take the radius of the drum to be 1.25 in and its axle to be horizontal)
A) 27
B) 0.4
C) 1.3
D) 8.0

Answer 1

Hint: Let us find the velocity at the top point so that complete rotation takes place without too fast or too slow. Next, the angular velocity can be found if we know the linear velocity. Finally, convert the angular velocity in rotations per minute by calculating it with required values and we will get the answer.

Formula used:
$\begin{align}
  & v=\sqrt{Rg} \\
 & \omega =\dfrac{v}{R} \\
\end{align}$

Complete answer:
Let us find the velocity at the top of the drum so that complete rotation takes place,
$v=\sqrt{Rg}$
the angular velocity is calculated as,
$\begin{align}
  & \omega =\dfrac{v}{R} \\
 & \omega =\sqrt{\dfrac{g}{R}} \\
 & \omega =\sqrt{\dfrac{10}{1.25}} \\
\end{align}$
The angular velocity in rotations per minute will be,
$\begin{align}
  & \omega (rpm)=\sqrt{\dfrac{10}{1.25}}\times \dfrac{60}{2\pi } \\
 & \omega (rpm)=27 \\
\end{align}$

So, the correct answer is “Option A”.

Additional Information:
There are different mix ratios of Concrete. Mix ratios are decided based upon the type of construction structures and mix designs. For Concrete Mix Ratio the components are — Cement, Sand, Coarse Aggregates and Water. Different Grades of Concrete denotes its strength for required construction. The proportion of the material is determined by the concrete mix expert in this method. In design mix the concrete production is with appropriate properties. In Design mix there is no guide for right mix proportions; it follows the economical method as per the requirement. It is followed by standard mixes — quantities of dry materials per cubic meter and by plunge.

Note:
Cement preparation plays an important role for a strong cement. The concrete must not be too wet. Portland cement is the best ingredient in concrete, and moisture does play an important role in preparation. Using old cement also turns out to be huge problems.