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QJEEM20Ph05f0: JEE Main 2020 Physics - Class 11 JEEM20Ph05f0 Solution: A bead of mass m stays at point P(a, b) on a wire bent in the…

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\omega (see figure). The value of ω\omega is (neglect friction) : JEE Main 2020 (Online) 2nd September Morning Slot Physics - Circular Motion Question 55 English

Multiple Choice Options

  • A 22gC2\sqrt {2gC}
  • B 2gC2\sqrt {gC}
  • C 2gCab\sqrt {{{2gC} \over {ab}}}
  • D 2gC\sqrt {{{2g} \over C}}

Step-by-Step Verified Solution

JEE Main 2020 (Online) 2nd September Morning Slot Physics - Circular Motion Question 55 English Explanation
y = 4Cx2

⇒\Rightarrow dydx\frac{dy}{dx} = tan θ\theta = 8Cx

At P, tan θ = 8Ca

For steady circular motion

mg sinθ = mω2acosθ

⇒\Rightarrow tan θ\theta = ω2ag\frac{\omega^{2} a}{g}

⇒\Rightarrow 8Ca ×\times g = ω2 ×\times a

⇒\Rightarrow ω\omega = 8gC\sqrt{8gC}

⇒\Rightarrow ω\omega = 22gC2\sqrt {2gC}

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