Concretemixture 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)
JEE MAIN 2016, Medium
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For just complete rotation
$v = \sqrt {Rg} $ at top point
The rotational speed of the drum
$ \Rightarrow \omega = \frac{v}{R} = \sqrt {\frac{g}{R}} = \sqrt {\frac{{10}}{{1.25}}} $
The maximum rotational speed of the drum in revolutions per minute
$\omega \left( {rpm} \right) = \frac{{60}}{{2\pi }}\sqrt {\frac{{10}}{{1.25}}} = 27.$
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