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Q.

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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a

$6 N$

b

$8 N$

c

$10 N$

d

$12 N$

answer is A.

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Detailed Solution

Question Image

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

(a) Centrifugal force $m ω^{2} r$

(b) Normal reaction $N = m g$

(c) Tangential reaction of the disk on the body = Coriolis force $2 m ω v$

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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A horizontal disc rotates with a constant angular velocity ω=6.0 rad/s about a vertical axis passing through its centre. A small body of mass m=0.50 kg moves along a diameter of the disc with a velocity v=50 cm/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 cm from the rotation axis.