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?

If all the particle of a system lie in a cube is it necessary that the centre of mass be in the cube?

The centre of mass is defined as vecR=1/Msum_im_ivecr_i . Suppose we define centre of charge as vecR_c=1/Qsum_iq_Ivecr_i where q_i represents the ith charge placed at vecr_i and Q is the total charge of the sytem a. Can a centre of charge of two charge system be outside the line segment joining the charges? b. If all the charges of a system are in X-Y plane? c. If all the charges of a system lie in a cube, is it necessary that the centre of charge be in the cube?

If all the particles of a system lie in y-z plane, the x-coordinate of the centre of mass will be zero. Is this statement true or false?

If large number of particles are distributed on XY plane and their centre of mass is at origin of coordinates, then

If a large number of particles are distributed on YZ plane and their centre of mass is at origin of coordinates, then Sum of moments of masses of all particles about the origin is zero Sum of momentum of masses of all particles w.r.t. the origin is zero Sum of moments of masses of all particles about Y axis is zero. Sum of moments of masses of all particles about Z axis is zero.

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 :-

x and y co-ordinates of a particle moving in x-y plane at some instant of time are x=2t and y=4t .Here x and y are in metre and t in second. Then The path of the particle is a…….

Two rods of equal lengths(l) and equal mass M are kept along x and y axis respectively such that their centre of mass lie at origin. The moment of inertia about an line y = x, is

Two bodies of masses 0.5 kg and 1 kg are lying in the X-Y plane at points (-1, 2) and (3, 4) respectively. Locate the centre of mass of the system.

The potential energy of a particle of mass 5 kg moving in the x-y plane is given by U=(-7x+24y)J , where x and y are given in metre. If the particle starts from rest, from the origin, then the speed of the particle at t=2 s is