Question

A wire frame is in the shape of a parabola $y=5x^2$. It is being rotated about y-axis with an angular velocity $\omega$. A small bead of ass $(m=1kg)$ is at point P and is in equilibrium with respect to the frame. Then the angular velocity $\omega$ is ($g=10m/s^2$)

• A. $\omega =5rad/sec$
• B. $\omega =10rad/sec$
• C. $\omega =20rad/sec$
• D. $\omega =15rad/sec$

Answer 1

The correct option is B $\omega =10rad/sec$

Given,

m=1kg

Equation of the curve:$y=5x^2$

Slope of tangent at $P(1,5)=$$y^{\prime }=10x{|}_{(1,5)}=10$

$⟹tan\theta =10$

Now from free body diagram, we get

For condition of equilibrium along the tangent

$m{\omega }^{2}rcos\theta =mgsin\theta$

$⟹\omega =\sqrt{\frac{gtan\theta }{r}}=10rad/sec$