A nucleus of mass 8 kg originally at rest emits particle of mass 4 kg with speed 2 m/s. The recoil speed of the nucleus is equal to

The problem can be solved using the principle of conservation of momentum.

The initial momentum of the system is zero because everything is at rest.

After the emission, the momentum of the system is the sum of the momentum of the nucleus and the momentum of the particle.

Momentum is given by the product of mass and velocity.

So, the momentum of the particle is 4 kg * 2 m/s = 8 kg*m/s.

Since the total momentum of the system must remain zero, the momentum of the nucleus must be -8 kg*m/s (it's negative because it's moving in the opposite direction of the particle).

The mass of the nucleus is 8 kg, so its velocity (or recoil speed) is -8 kg*m/s / 8 kg = -1 m/s.

The negative sign indicates that the direction of the velocity is opposite to the direction of the particle.

So, the recoil speed of the nucleus is 1 m/s.