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  4. A coin placed on a rotating turn table just slips if it is placed at a distance of 4 cm from the centre. If the angular velocity of the turn table is doubled it will just slip at a distance of

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Q. A coin placed on a rotating turn table just slips if it is placed at a distance of $4\, cm$ from the centre. If the angular velocity of the turn table is doubled it will just slip at a distance of

KCETKCET 2021Laws of Motion

Solution:

$r =4 \,cm$
$f = mr \omega^{2}$
$f =\mu mg$
$\mu mg = m \omega^{2} r$
$\mu g =\omega^{2} r$
$\mu g =\omega^{2} \times 4$ ... (1)
$\omega^{1}=2 \omega$
$\mu g =(2 \omega)^{2} r$
$\mu g =4 \omega^{2} r$ ... (2)
$\omega^{2} \times 4=4 \omega^{2} r$
$r =1 \,cm$