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A small object placed on a rotating horizontal turn-table just slips when it is placed at a distance of 4 cm from the axis of rotation. If the angular velocity of the turn-table is doubled then the object slips when its distance from the axis of rotation is

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a

1cm

b

2 cm

c

4 cm

d

8 cm

answer is A.

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Detailed Solution

The object will not slip if the centripetal force is equal to or greater than force of friction, i.e.,mvb24≥μR or mω2r≥μmgor ω2r≥μg or r∝1/ω2∴ r2r1=ω1ω22 or r2=r1ω1ω22or, r2=4×ω12ω2=1cm

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