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 m and its axle to be horizontal) :

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 m and its axle to be horizontal) : (A) 0.4 (B) 1.3 (C) 8.0 (D) 27.0

Tardigrade Admin · Accepted Answer

For just complete rotation, v =√ Rg at top point ⇒ w =( v / R )=√( g / R )=√(10/1.25) ω( rpm )=(60/2 π) √(10/1.25)=27

0.4

1.3

8.0

27.0

For just complete rotation, v=Rg​ at top point ⇒w=Rv​=Rg​​=1.2510​​ ω(rpm)=2π60​1.2510​​=27

For just complete rotation,
$v = R g$ at top point
$\Rightarrow w = \frac{v}{R} = \frac{g}{R} = \frac{10}{1.25}$
$ω (r p m) = \frac{60}{2 π} \frac{10}{1.25} = 27$