Physics, Chemistry, Mathematics Forums

A) When the two bodies going to collide are coming towards each other or one coming towards other and other going away from first, if their velocities are along same line, then the collision is said to be head-on.

B) Yes, the centre of mass lies in the same plane in which the body lies. This is because, the com has the same no. of co-ordinates as the no. of dimensions of the plane : For X-Y plane, X_com = Sum(m_ix_i)/M_sys and Y_com = sum(m_iy_i)/M_sys and
Z_com = sum(m_iz_i)/M_sys = 0 as z_i = 0. Thus, com necessarily lies in X-Y Plane.

c) Yes, for symmitrical and uniform bodies, the com is the geometrical centre of the body which for a cube lies inside it. Even if the mass distribution is not uniform, the com would lie somewhere inside the cube only b'couz  the mass  is inside the cube only.

d) No, the linear momentum cannot be conserved in a non-inertial frame. This is because in a non-inertial frame, the bodies experience a force due to acc. of the frame.

e)No, the bodies in a non-inertial frame woul be experiencing some net force and thus there vel. would be varying. So, the rel. vel. of sep. = e X vel. of app. wouldn't hold good.

f)A particle is an infinitely small body where as a rigid body is a collection of a no. of point objects. The rotational mechanics does not hold good for a point obj. while it does so for rigid bodies.

1)Head-on collision means that the bodies mentioned move in the same straight line and the direction of their velocities is opp to each other.

2)

let origin be at M1 then Xcm for M1& M2 only=1/(M1+M2) *M2X2 which is less than X2 always as D^r>N^r.Similarly consider each two particle system and it can be shown that cm(Centre Of mass) lies between them.Finally find cm of all cm's.It will be less than Xn.Thus proved that cm lias inside body.

Extend this idea to Ycm and Zcm will be 0 as Z-coordinate of all the masses is 0.Thus cm lies in XY-plane.

3)Extend above idea to Zcm.It lies inside cube.

4)For conservation of linear momentum it is necessary that F_ext=0 on the system(Consult HC VERMA).When we write equations from non-inertial frames,we have to include pseudo force.Thus Fext is not 0.Thus L is not constant.Thus we can't apply conservation of linear momentum.

5)the result “velocity of approach = velocity of separation” is true only elatic collision between two bodies.Your question seems to be incomplete as I don't see two bodies.

6)A particle is a point object which has a definite mass.A rigid body is a group of paricles.A rigid body can be treated as a particle by showing all the foces on it through cm to apply Newton's laws.Torque is talked always for rigid bodies and not for particles. All particles of rigid body preserve their positions wrt each other when force is app. to it.