Question

A particle initially at rest is acted upon by force $\overrightarrow{F}$ = – F₀coswt $\widehat{i}$ – F₀ sin wt $\widehat{j}$ + F₀$\widehat{k}$. The trajectory of particle will be –

• A. Helix with uniform pitch
• B. Helix with non-uniform pitch
• C. Circle with changing radius (spiral)
• D. Cycloid

Answer 1

Answer: (B)

Helix with non-uniform pitch

Answer 2

In X Y plane

$\overrightarrow{F}$ = – F₀ cos t $\widehat{i}$ – F₀ sin t $\widehat{j}$

= – F₀ ${\widehat{e}}_{r}$ e_r = unit vector in radial direction

 Path will be circular in X – Y plane

Superimposing motion along Z-axis, path will be helical with non-uniform pitch.