First slide

Oscillation motion

Question

A particle is moving in a circle of radius R = 1 m with constant speed v = 4 m/s. The ratio of the displacement to acceleration of the foot of the perpendicular drawn from the particle onto the diameter of the circle is

Easy

A

$\large \frac{1}{{16}}{s^2}$
B

$\large \frac{1}{2}{s^2}$
C

$\large 2{s^2}$
D

$\large 16{s^2}$

Solution

$\large \frac{s}{a}\, = \,\frac{s}{{{\omega ^2}s}}\, \Rightarrow \,\left[ {a = {\omega ^2}s} \right]\, \Rightarrow \,\frac{s}{a}\, = \,\frac{1}{{{\omega ^2}}}$
$\large v\, = \,R\omega \, \Rightarrow 4\, = \,1w\, \Rightarrow w\, = \,4rad/\sec$
$\large \frac{s}{a}\, = \,\frac{1}{{16}}$

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