If all the particle of a system lie in X-Y plane is it necessary that the centre of mass be in X-Y plane?

.Does the velocity of all particles of a system is equal to the velocity of centre of mass?..

The potential energy of a particle of mass 1 kg moving in X-Y plane is given by U=(12x+5y) joules, where x an y are in meters. If the particle is initially at rest at origin, then select incorrect alternative :-

Three rods each of mass m and length l are joined together to form an equilateral triangle as shown in figure. Find the moment of inertial of the system about an axis passig through its centre of mass and perpendicular to the plane of the particle.

Comprehension # 5 One particle of mass 1 kg is moving along positive x-axis with velocity 3 m//s . Another particle of mass 2 kg is moving along y-axis with 6 m//s . At time t = 0, 1 kg mass is at (3m, 0) and 2 kg at (0, 9m), x - y plane is the horizontal plane. (Surface is smooth for question 1 and rough for question 2 and 3) The centre of mass of the two particles is moving in a straight line which equation is :-

Comprehension # 5 One particle of mass 1 kg is moving along positive x-axis with velocity 3 m//s . Another particle of mass 2 kg is moving along y-axis with 6 m//s . At time t = 0, 1 kg mass is at (3m, 0) and 2 kg at (0, 9m), x - y plane is the horizontal plane. (Surface is smooth for question 1 and rough for question 2 and 3) Co-ordinates of centre of mass where it will stop finally are :-

Comprehension # 5 One particle of mass 1 kg is moving along positive x-axis with velocity 3 m//s . Another particle of mass 2 kg is moving along y-axis with 6 m//s . At time t = 0, 1 kg mass is at (3m, 0) and 2 kg at (0, 9m), x - y plane is the horizontal plane. (Surface is smooth for question 1 and rough for question 2 and 3) If both the particles have the same value of coefficient of friction mu = 0.2 . The centre of mass will stop at time t = ..........s :-

A particle projected from origin moves in x-y plane with a velocity vecv=3hati+6xhatj , where hati" and "hatj are the unit vectors along x and y axis. Find the equation of path followed by the particle :-

A particle is projected in x-y plane with y- axis along vertical, the point of projection being origin. The equation of projectile is y = sqrt(3) x - (gx^(2))/(2) . The angle of projectile is ……………..and initial velocity is ………………… .

A small particle of mass m is fixed to the perimeter of a ring of same mass and radius r. The system comprising of particle and ring is placed on a horizontal plane. Friction is negligible on horizontal plane. Initially particle is at top most point, then the system is released from rest. Answer next two question when the particle is at the same height as the centre of ring aftr being released from top most point. Assume that the ring stays in vertical plane during its motion under consideration Mark the CORRECT option(s):-

A small particle of mass m is fixed to the perimeter of a ring of same mass and radius r. The system comprising of particle and ring is placed on a horizontal plane. Friction is negligible on horizontal plane. Initially particle is at top most point, then the system is released from rest. Answer next two question when the particle is at the same height as the centre of ring aftr being released from top most point. Assume that the ring stays in vertical plane during its motion under consideration Mark the CORRECT option(s):