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A horizontal disc rotates with a constant angular velocity $ω = 6.0 r a d / s$ about a vertical axis passing through its centre. A small body of mass $m = 0.50 k g$ moves along a diameter of the disc with a velocity $v = 50 c m / s$ which is constant relative to the disc. Find the force that the disc exerts on the body at the moment when it is located at the distance $r = 30 c m$ from the rotation axis.

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$8 N$

$10 N$

$12 N$

$6 N$

answer is A.

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Detailed Solution

. The body will experience three mutually perpendicular forces in the rotating table.

(a) Centrifugal force $m ω^{2} r$

(b) Normal reaction $N = m g$

Force exerted by the disk on the body = $\sqrt{{(m g)}^{2} + {(2 m ω v)}^{2}} = 5.83 N ≃ 6 N$

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