Question

A particle of mass 5 × 10^-5 kg is placed at the lowest point of a smooth parabola having the equation 20x² = y (x, y in m). Here y is the vertical height. If it is displaced slightly and is constrained to move along the parabola, the angular frequency (in rad/s) of small oscillations is ______.

पर्याय

• 10.00

• 20.00

• 30.00

• 40.00

Answer 1

A particle of mass 5 × 10^-5 kg is placed at the lowest point of a smooth parabola having the equation 20x² = y (x, y in m). Here y is the vertical height. If it is displaced slightly and is constrained to move along the parabola, the angular frequency (in rad/s) of small oscillations is 20.00.

Explanation:

The potential energy of particle = mgy

∴ `F_x = (-∂U)/(∂x)`

= `(-∂(20mgx^2))/(∂x)`

= -40 mgx

F ∝ -x, thus

`omega^2 = (40 xx 5 xx 10^-5 xx 10)/(5 xx 10^-5)`

⇒ ω = 20 rad s^-1