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Question:

A particle moves in x-y plane according to rule x = asinωt and y = acosωt. The particle follows:

an elliptical path

a circular path

a parabolic path

a straight line path inclined equally to x and y-axes

Solution:

x = asinωt or x/a = sinωt.. (i)
y = acosωt or y/a = cosωt.. (i)
Squaring and adding, we get
x²/a² + y²/a² = 1 (∵cos²ωt + sin²ωt = 1)
or
x² + y² = a²
This is the equation of a circle. Hence particle follows a circular path.