Question

A particle of mass $5\times {10}^{-5}$ kg is placed at the lowest point of a smooth parabola having the equation $x^2=40y$ (x,y in cm). If it is displaced slightly and it moves such that it is constrained to move along the parabola , the angular frequency of oscillation will be, approximately

• A. $1s^{-1}$
• B. $7s^{-1}$
• C. $5s^{-1}$
• D. None of these

Answer 1

Answer: (D)

None of these

At x, $tan\left(\theta \right)=\frac{dy}{dx}=\frac{x}{20}$,

Also $F=ma=-mgsin\left(\theta \right)\approx -mg\theta$ since $\theta$ is small,

$a=-g\theta =-\frac{gx}{20}=-\frac{x}{2}$

Since $a=-{\omega }^{2}x$,

$\omega =\frac{1}{\sqrt{2}}{s}^{-1}$