A coin placed on a rotating table just slips when it is placed at a distance of 1   cm from the centre.…

A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the centre. If the angular velocity of the table is halved, it will just slip when placed at a distance of _____ from the centre:
  1. 8 cm
  2. 4  cm
  3. 1 cm
  4. 2 cm

Solution

The coin will slip when 

μmg=mω2r

μg=ω2×1 cm   ...(i)

Now, ω'=ω2

μg=ω22R   ...(ii)

Hence we can write from (i) and (ii)

ω2×1 cm=ω24RR=4 cm

Asked in: JEE Main 2023 (11 Apr Shift 1)

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