When a disc is rotating with angular velocity ω , a particle situated at a distance of 4 cm just begins to slip. If the angular velocity is doubled, at what distance will the particle start to slip?

Question

When a disc is rotating with angular velocity ω , a particle situated at a distance of 4 cm just begins to slip. If the angular velocity is doubled, at what distance will the particle start to slip? (A)  1 cm  (B)  2 cm  (C)  3 cm  (D)  4 cm

Tardigrade Admin · Accepted Answer

Angular velocity =ω Centripetal force F=m r ω2 Or r propto (1/ω2) ∴ (r1/r2)=(ω22/ω12) or (4/r2)=(4 ω2/ω2) or r2=1 cm

Q. When a disc is rotating with angular velocity $ω$ , a particle situated at a distance of $4 c m$ just begins to slip. If the angular velocity is doubled, at what distance will the particle start to slip?

$1 c m$

$2 c m$

$3 c m$

$4 c m$

Angular velocity $= ω$
Centripetal force $F = m r ω^{2}$
Or $r \propto \frac{1}{ω ^{2}}$
$∴ \frac{r _{1}}{r _{2}} = \frac{ω _{2}^{2}}{ω _{1}^{2}}$
or $\frac{4}{r _{2}} = \frac{4 ω ^{2}}{ω ^{2}}$
or $r_{2} = 1 c m$

Q. When a disc is rotating with angular velocity ω , a particle situated at a distance of 4cm just begins to slip. If the angular velocity is doubled, at what distance will the particle start to slip?

1cm

2cm

3cm

4cm