A bead of mass m stays at point P(a, b) on a wire bent in the shape of a parabola y=4 C x2 and rotating with angular speed ω (see figure). The value of ω is (neglect friction) :

Question

A bead of mass m stays at point P(a, b) on a wire bent in the shape of a parabola y=4 C x2 and rotating with angular speed ω (see figure). The value of ω is (neglect friction) : (A) √(2 gC / ab ) (B) 2 √2 gC  (C) √(2 g / C ) (D) 2 √ gC

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/40af319890851c57a0524595a46ca138-.png" /> m x ω2 cos θ=m g sin θ x ω2=g tan θ x ω2=g ⋅ (d y/d x) x ω2=g ⋅(8 c x) ω2=8 g c ω=2 √2 g c

Q. A bead of mass $m$ stays at point $P (a, b)$ on a wire bent in the shape of a parabola $y = 4 C x^{2}$ and rotating with angular speed $ω$ (see figure). The value of $ω$ is (neglect friction) :

$\frac{2 g C}{ab}$

$2 2 g C$

$\frac{2 g}{C}$

$2 g C$

$m x ω^{2} cos θ = m g sin θ$
$x ω^{2} = g tan θ$
$x ω^{2} = g \cdot \frac{d y}{d x}$
$x ω^{2} = g \cdot (8 c x)$
$ω^{2} = 8 g c$
$ω = 2 2 g c$

Q. A bead of mass m stays at point P(a,b) on a wire bent in the shape of a parabola y=4Cx2 and rotating with angular speed ω (see figure). The value of ω is (neglect friction) :

ab2gC​​

22gC​

C2g​​

2gC​