4. Two masses 2kg and 3kg that are attached to each other slide together as a unit, and then break apart (as shown below). If the final velocity for m2 is 10m/s after breaking,

To find the final velocity for m2 after breaking, we need to apply the law of conservation of momentum. According to this law, the total momentum before the break should be equal to the total momentum after the break.

The momentum of an object can be found by multiplying its mass by its velocity. Therefore, the momentum of m1 before the break is given by m1v1, where m1 is the mass of m1 and v1 is its velocity before the break. The momentum of m2 before the break is given by m2v2, where m2 is the mass of m2 and v2 is its velocity before the break.

Since the two masses are attached together, their velocity before the break is the same, let's call it v0.

So, the total momentum before the break is (m1v0 + m2v0).

After the break, the masses separate, and m2 has a final velocity of 10m/s. Therefore, the total momentum after the break is given by the sum of the momentum of m1 and the momentum of m2.

The momentum of m1 after the break is given by m1 * 0 (assuming it comes to rest).

Therefore, the total momentum after the break is (m1 * 0 + m2 * 10). According to the law of conservation of momentum, this should be equal to the total momentum before the break.

Setting up the equation:
(m1v0 + m2v0) = (m1 * 0 + m2 * 10)

Now we can solve for v0, the initial velocity of both masses.

v0 * (m1 + m2) = m2 * 10

Dividing both sides by (m1 + m2):

v0 = (m2 * 10) / (m1 + m2)

Substituting values, m1 = 2kg, m2 = 3kg:

v0 = (3kg * 10m/s) / (2kg + 3kg)

v0 = 30kg.m/s / 5kg

v0 = 6m/s

Therefore, the initial velocity of both masses before the break is 6m/s.