Is centre of mass always a reality ?

A : A bomb at rest explodes. The centre of mass of fragments moves along parabolic path. R : Under the effect of gravity only the path followed by centre of mass is always parabolic.

The centre of mass always lies on the axis of symmetry if it exists. Is this statement true or false?

As the temperature is increased, the period of a pendulum a) Increases as its effective length increases even through its centre of mass still remains at the centre of the bob. b) decreases as its effective length increases even though its centre of mass still remains at the centre of the bob. c) Increases as its effective length increases due to shifting of centre of mass below the centre of the bob. d) decreases as its effective length remains same but the centre of mass shifts above the centre of the bob.

Assertion : Moment of inertia about an axis passing throught centre of mass is always minimum Reason : Theorem of parallel axis can be applied for 2-D as well as 3-D bodies.

Assertion : Moment of inertia about an axis passing throught centre of mass is always minimum Reason : Theorem of parallel axis can be applied for 2-D as well as 3-D bodies.

The centre of mass of a body

Statement-1 : The centre of mass of a body may lie where there is no mass. Statement-2 : The centre of mass has nothing to do with the mass.

Considering a system having two masses m_(1) and m_(2) in which first mass is pushed towards centre of mass by a distance a, the distance required to be moved for second mass to keep centre of mass at same position is :-

Two particles of masses m and 3m approach each other with different velocities. After collision, the particle of mass m has velocity vec( v) in their centre of mass frame. Velocity of particle of mass 3m in the centre of mass frame is

Does centre of mass and centre of gravity body always coincide?