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 be on a straight line with slope 4/3
C. motion will be a simple harmonic along x-axis with amplitudes 5.
D. phase difference between two motion is `pi//2`

Answer

B

Explanation

`x=3 sin 100 pi t`
`y=4 sin 100 pit`
Equation of path is ltbRgt `y/x=4/3 i.e., y=4/3 x`
Which is equation of straight line having slope `4/3`
Equation of resulting motion is `vec(r)=xhati+yhatj=(3hati+4hatj) sin 100 pit`
Amplitude is `sqrt(3^(2)+4^(2)) =5`