Motion of a particle in x – y plane is described by a set of following equations x = 4sin (π2−ωt) m and y = 4sin (ωt)m. The path of a particle will be

x=4sin (π2−ωt) - (i) y=4sin (ωt) - (ii) From (i) and (ii) cos2 ωt+sin2ωt= (x4)2+ (y4)2=1 ⇒x2+y2= (4)2

Motion of a particle in x – y plane is described by a set of following equations x = 4sin $(\frac{π}{2} - ω t)$ m and y = 4sin $(ω t) m .$ The path of a particle will be

Option 1 - circular

Option 2 - helical

Option 3 - parabolic

Option 4 - elliptical

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Payal Gupta | Contributor-Level 10

6 months ago

Correct Option - 1

Detailed Solution:

$x = 4 s i n (\frac{π}{2} - ω t)$ - (i)

$y = 4 s i n (ω t)$ - (ii)

From (i) and (ii) cos2 $ω t + s i n^{2} ω t = {(\frac{x}{4})}^{2} + {(\frac{y}{4})}^{2} = 1$

$\Rightarrow x^{2} + y^{2} = {(4)}^{2}$

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