Momentum is conserved if and only if sum of all forces which are exserted on system equals zero. In our situation there are only internal forces, so by Newton's third law their vector sum is 0.
So 
.
Kinetic energy of system at first: 
. After: 
. The secret is that other energy is in work of deformation forces (they in turn heat a bullet and a block).
Answer is A)
1)
p = 2.4 * 10^5 Pa
T = 18° C + 273.15 = 291.15 k
r = 0.25 m => V = [4/3]π(r^3) = [4/3]π(0.25m)^3 = 0.06545 m^3 = 65.45 L
Use ideal gas equation: pV = nRT => n = pV / RT = [2.4*10^5 Pa * 0.06545 m^3] / [8.31 J/k*mol * 291.15k] = 6.492 mol
Avogadro number = 1 mol = 6.022 * 10^23 atoms
Number of atoms = 6.492 mol * 6.022 *10^23 atom/mol = 39.097 * 10^23 atoms = 3.91 * 10^24 atoms
2) Double atoms => double volume
V2 / V1 = r2 ^3 / r1/3
2 = r2 ^3 / r1 ^3 => r2 ^3 = 2* r1 ^3
r2 = [∛2]r1
The factor is ∛2
