A particle moves in x-y plane according to ru le x`=a sin omegat` and y=`a cos omegat`. The particles follows:

Options

A. an elliptical path
B. a circular path
C. a parabolic path
D. a straight line path inclined equally to x and y-axes.

Answer

B

Explanation

`x = a sin omegat " or " x/a = sin omega t " "...(i)`
`y = a cos omegat " or " y/a = cos ommegat " "...(ii)`
Squaring and adding equation (i) and (ii), we get
`x^2/a^2+y^2/a^2=1 " "( :.cos^(2)omegat+sin^(2)omegat=1)`
or `x^2 +y^2 =a^(2)`
This is the equation of a circle. Hence particle follows a circular path.