Momentum of first ball = Momentum of the second ball
m1 v1 = m2 v2
5 × 7 = 2 × v2        v2 = 35/2 m/s
Velocity of centre of mass:
vcm=m1v1+m2v2/m1+m2 =5×7+2×35/2/5+2
=10m/s

Problem:
Two blocks of masses 5 kg and 2 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse provides a velocity of 7 m/s to the heavier block in the direction of the lighter block. Find the velocity of the center of mass.

Solution:
To find the velocity of the center of mass, we need to determine the total momentum of the system and divide it by the total mass of the system.

Step 1: Identify the given information
- Mass of the first block (m1): 5 kg
- Mass of the second block (m2): 2 kg
- Impulse provided: 7 m/s

Step 2: Calculate the momentum of each block
The momentum of an object is given by the product of its mass and velocity.

- Momentum of the first block (p1): m1 * v1
- Momentum of the second block (p2): m2 * v2

Step 3: Apply the principle of conservation of momentum
According to the principle of conservation of momentum, the total momentum before the impulse is equal to the total momentum after the impulse.

- Total momentum before the impulse: p1 + p2
- Total momentum after the impulse: (m1 * v1) + (m2 * v2)

Step 4: Determine the velocities
Since the impulse only affects the velocity of the first block, we can write the equation:

(m1 * v1) + (m2 * v2) = (m1 * v1') + (m2 * v2')

Where v1' and v2' are the final velocities of the first and second block, respectively.

Given that the impulse provides a velocity of 7 m/s to the first block (heavier block) in the direction of the second block (lighter block), we have:

v1' = 7 m/s
v2' = -7 m/s (negative sign indicates the opposite direction)

Step 5: Solve for the velocities
Substituting the given values into the equation:

(5 * v1) + (2 * v2) = (5 * 7) + (2 * -7)
5v1 + 2v2 = 35 - 14
5v1 + 2v2 = 21

Since the spring connecting the blocks has negligible mass, the forces between the blocks are internal and do not affect the center of mass. Therefore, the center of mass will maintain the same velocity as before the impulse.

Step 6: Calculate the velocity of the center of mass
To find the velocity of the center of mass, we divide the total momentum by the total mass of the system:

Total momentum = (m1 * v1') + (m2 * v2')
Total mass = m1 + m2

Velocity of the center of mass = Total momentum / Total mass

Substituting the known values:

Velocity of the center of mass = ((5 * 7) + (2 * -7)) / (5 + 2)
Velocity of the center of mass = (35 - 14) / 7
Velocity of the center of mass = 21 / 7
Velocity of the