Question

A particle moves in the X-Y plane according to the equation  vector r = (vector i + 2vector j ) A cosωt. The motion of the particle is 

(a) on a straight line 

(b) on an ellipse

(c) periodic 

(d) simple harmonic.

Answer 1

(a) on a straight line 

(c) periodic 

(d) simple harmonic.

EXPLANATION: 

 r=A.cos⍵t is the equation of an SHM, i+2j is the direction of a straight line. So the given equation is the simple harmonic motion of the particle on a straight line, hence also periodic. So (a), (c) and (d) are true.  When the motion is on the straight line it can't be on an ellipse, so (b) is not true.