A block of mass M is moving on a smooth horizontal surface with constant speed u. Bullets arefired horizontally against the block to reduce the velocity of the block to half its initial value.Bullets get embedded in the block. Mass of each bullet is ‘m’ and speed ‘u’. Then the number ofbullets required is–

Since there is no external force acting on the system during collision, the linear moment of bullet+block system will be conserved.

Initial momentum of block=
Final momemntum of block after its speed gets reduced to half=

The reduction of momentum will be imparted by the incoming bullets in the direction opposite to that of the block. Let the number of bullets be.

Hence