Question

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)

विकल्प

• 2`sqrt"gC"`

• `sqrt(2"gC")/"ab"`

• `sqrt(2"g")/"C"`

• 2`sqrt(2"gC")`

Answer 1

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 2`sqrt(2"gC")`.

Explanation:

y = 4Cx²

⇒ `dy/dx` = tan θ = 8Cx

At P, tan θ = 8Ca

For steady circular motion

mg sinθ = mω²acosθ

⇒ tan θ = `(omega^2"a")/"g"`

⇒ 8Ca × g = ω² × a

⇒  ω = `sqrt(8"gC")`

⇒  ω = `2sqrt(2"gC")`