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Q.

Column-I shown position vector as function of  time for a particle. Match the  characteristic of the motion with their description in column-II

 COLUMN-I COLUMN-II
aA particle has its position as a function of  time given by  r(t)=r0+v0t  where  r0  and  v0  are non-zero constants.pAngular momentum of the system about the origin is conserved.
bA particle has its position vector as function of time given by  r(t)=v0tk^+(c0cosωt)i^ +(c0sinωt)j^
 where a0  and  v0  are non-zero constant, (angle between  v0 and  a0   is 90°<θ<180°  
qThe particle  may be charged and moving in a uniform magnetic field no other force acts on it.
cA particle is moving in a plane with its position vector  given by r(t)=(a0sinωt)i^+(b0cosωt)j^  where  a0,b0(a0b0)  and  ω  are positive constant.rProjection of particle on x or y axis is simple harmonic motion
dA particle is moving in a plane with Position vector r(t)=(a0cosωt)i^+(a0sinωt)j  where  a0 and  ω  are positive constantsKinetic energy of the particle is constant.
  tArea swept by position vector of particle in equal time interval is equal.

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a

a-p,s,t;  b-,q,r,s,; c-r,s;  d-p,q,r,s,

b

a-q,t; b-p,q ; c-q,r;  d-r,s,t

c

a-p,q,r,t; b-p,,r,s,t;  c-p,r;  d-q,r,s,

d

a-p,q,s,t;   b-p,q,r,s,t;   c-r;  d-p,q,r,s,t

answer is D.

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Detailed Solution

Since mechanical energy is conserved, balls will have same potential energy at the same height and 
thus will have same kinetic energy.

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