A horizontal turn table is rotating at some angular velocity. An object just slips when it is placed at a distance 4 cm from the axis of rotation. Now, the angular velocity of the turn-table is doubled. The object will slip when it's distance from the axis of rotation is:

Question

A horizontal turn table is rotating at some angular velocity. An object just slips when it is placed at a distance 4 cm from the axis of rotation. Now, the angular velocity of the turn-table is doubled. The object will slip when it's distance from the axis of rotation is: (A) 1 cm (B) 2 cm (C) 4 cm (D) 8 cm

Tardigrade Admin · Accepted Answer

The object will slip if centripetal force â¥ force of friction mrω 2>μ mg rω 2≥ μ g r(ω )2≥ constant,or ((r1/r2))=(((ω )2/(ω )2))2 (4 c m/r2)=((2 ω /ω ))2∴ r2=1 cm

Q. A horizontal turn table is rotating at some angular velocity. An object just slips when it is placed at a distance $4 c m$ from the axis of rotation. Now, the angular velocity of the turn-table is doubled. The object will slip when it's distance from the axis of rotation is:

$1$ $c m$

$2$ $c m$

$4$ $c m$

$8$ $c m$

The object will slip if centripetal force ≥ force of friction
$m r ω^{2} > μ m g$
$r ω^{2} \geq μg$
$r (ω)^{2} \geq co n s t an t, or (\frac{r _{1}}{r _{2}}) = (\frac{( ω ) _{2}}{( ω ) _{2}})^{2}$
$\frac{4 c m}{r _{2}} = (\frac{2 ω}{ω})^{2} ∴ r_{2} = 1 c m$

Q. A horizontal turn table is rotating at some angular velocity. An object just slips when it is placed at a distance 4cm from the axis of rotation. Now, the angular velocity of the turn-table is doubled. The object will slip when it's distance from the axis of rotation is:

1 cm

2 cm

4 cm

8 cm