A particle is subjected to two simple harmonic motions along x and y directions according to and `x = 3 sin 100 pit y = 4 sin 100 pit`

Options

A. Motion of particle will be on ellipse traversing it in clockwise direction.
B. Motion of particle will on a straight line with slope `4//3`
C. Motion will be a simple harmonic motion along x-axis with amplitude 5.
D. Phase difference between two motions is `pi//2`

Answer

B

Explanation

`x = 3 sin 100 pi t`
`y = 4 sin 100 pi t`
Equation of path is
`(y)/(x) = (4)/(3)` i.e. `y = (4)/(3) x`
which is equation of a straight line having slope `(4)/(3)`
Equation of resulting motion is `vec(r) = x hat(i) + y hat (j)`