Concrete mixture is made by mixing cement, stone and sand in a… | JEE Main 2016 (10 Apr, Shift 1)

Q14JEE Main 2016 · 10 APR · SHIFT 1Medium

Level Road & Rotating Platform

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):

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Answer: (d)

With a horizontal axle, material sticks if at the top $m\omega^2 R \ge mg$ . For mixing, $\omega < \sqrt{\frac{g}{R}}$ .
$\omega_{max} = \sqrt{\frac{9.8}{1.25}} = \sqrt{7.84} = 2.8$ rad/s
rpm $= \frac{2.8 \times 60}{2\pi} \approx 26.7 \approx 27$
So the answer is (d) 27.0.

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