JEE MAIN - Physics (2016 - 10th April Morning Slot - No. 18)
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) :
(Take the radius of the drum to be 1.25 m and its axle to be horizontal) :
0.4
1.3
8.0
27.0
Paaiškinimas
For proper mixing, the concrete mixture should not stick to the top wall of the cylinder and it should fall down.
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The maximum velocity at the top is v, then we have
$${{m{v^2}} \over r} = mg$$
$$ \Rightarrow v = \sqrt {rg} $$
Therefore, the maximum rotational speed of the drum is
$$\omega = {v \over r} = \sqrt {{g \over r}} = \sqrt {{{9.8} \over {1.25}}} $$ rad/s
$$ = \sqrt {{{9.8} \over {1.25}}} \times {{60} \over {2\pi }}$$ rpm = 26.74 $$\approx$$ 27 rpm