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

Question

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 (A) 1 cm (B) 2 cm (C) 4 cm (D) 8 cm

Tardigrade Admin · Accepted Answer

r =4 cm f = mr ω2 f =μ mg μ mg = m ω2 r μ g =ω2 r μ g =ω2 × 4 ... (1) ω1=2 ω μ g =(2 ω)2 r μ g =4 ω2 r ... (2) ω2 × 4=4 ω2 r r =1 cm

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

1 cm

2 cm

4 cm

8 cm

$r = 4 c m$
$f = m r ω^{2}$
$f = μ m g$
$μ m g = m ω^{2} r$
$μg = ω^{2} r$
$μg = ω^{2} \times 4$ ... (1)
$ω^{1} = 2 ω$
$μg = (2 ω)^{2} r$
$μg = 4 ω^{2} r$ ... (2)
$ω^{2} \times 4 = 4 ω^{2} r$
$r = 1 c m$

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