about the second question which was ∶ a bomb initially at rest ,explodes into several pieces .(a)is linear momentum conserved ?(b)is kinetic energy conserved ?
explane ?
My answer is∶ the momentum is not conserved ?but the kinetic energy is conserved because the kinetic energy of all picese qual
to the chemical potential enegry which was into the bomb before exploding . ( i am not sure about this answer )

Let's get momentum cleared up first.
Momentum is conserved.
Initially the bomb is at rest so has zero momentum in any direction
Momentum is a vector quantity.
Hence direction is also important.
I see from your formulae that you understand momentum can be positive or negative.
So the momentum equation for the explosion event is:
Vector sum of momentum after explosion = Vector sum before explosion = 0 in this case.
You will find that the vector sum, taking signs into account, of the moementa of all the fragments adds up to zero.
Of course we add the components in three mutually perpendicular directions, where they will separately add to zero in each of those directions.
Now for the energy.
The question asks specifically for the kinetic energy.
Again initially the bomb is at rest so the kinetic energy is initially zero.
So yes the total of chemical and kinetic energies (and any others that may be involved) is constant ie preserved.
But the kinetic energy is one half mass (always positive) times the velocity squared (again always positive).
KE is always positive.
So the kinetic energies of all the fragments are all positive (unlike the momenta)
And they are moving so their sum is not zero.
So kinetic energy is not conserved
This is why it is so useful to have both momentum and KE available for calculation.
Would you like to revisit your other answers in the light of this?