A moving body of mass $m$ and velocity $3\, km / hr$. Collides with a body at rest and of mass $2\, m$ and then sticks to it. Now the combined mass starts to move, then the combined velocity will be :

Question

A force of 10 N is applied to move a body of mass 5 kg over a distance of 3 meters. Find the work done by the force.

Answer 1

To solve this problem, we will employ the principle of conservation of momentum. According to this principle, the total momentum before the collision equals the total momentum after the collision when no external forces are acting.

Step 1: Calculate initial momentum

The initial momentum of the system is the sum of the momenta of both bodies before the collision. The body with mass $m$ is moving with a velocity of $3 \, \text{km/hr}$, and the other body with mass $2m$ is at rest.

Momentum of the first body = m \times 3 = 3m \, \text{km/hr}
Momentum of the second body = 2m \times 0 = 0 \, \text{km/hr}

Total initial momentum = 3m \, \text{km/hr}

Step 2: Calculate final momentum

After the collision, the two bodies stick together and move as a single body with a combined mass of 3m.

Let the final velocity of the combined mass be v.

Total momentum after collision = 3m \times v \, \text{(km/hr)}

Step 3: Apply the conservation of momentum

According to the conservation of momentum:

3m = 3m \times v

Dividing both sides by 3m:

1 = v

The velocity v of the combined mass after the collision is 1 \, \text{km/hr}.

Conclusion:

The combined velocity of the two bodies after the collision is 1 \, \text{km/hr}. Therefore, the correct answer is 1 km/hr.

Answer 2