Work Energy Power

JEE Main level, single correct, medium

177 of 183

Question 177 of 183

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: (A) 27.0

To break the circular motion max velocity at top point

vmax⁡=Rg{v}_{\max }=\sqrt{Rg}

⇒wmax⁡=vmax⁡R=gR=101.25\Rightarrow {w}_{\max }=\dfrac{{v}_{\max }}{R}=\sqrt{\dfrac{g}{R}}=\sqrt{\dfrac{10}{1.25}}

wmax⁡(rpm)=602π101.25=27{w}_{\max }\left(rpm\right)=\dfrac{60}{2\pi }\sqrt{\dfrac{10}{1.25}}=27

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