Question

In a perfectly inelastic head on collision

• A. kinetic energy is conserved
• B. total energy is not conserved
• C. linear momentum is not conserved
• D. two bodies move as one body after collision
• E. two bodies move separately in different directions

Hint:

Perfectly inelastic collision = bodies stick together. Momentum conserved, kinetic energy not conserved.

Answer 1

The Correct Option is D

Step 1: Understand perfectly inelastic collision.
In a perfectly inelastic collision, the colliding bodies stick together after collision.
This means they move with a common velocity as a single combined mass.

Step 2: Check conservation laws.
In all types of collisions: \[ \text{Linear momentum is conserved} \] However, in inelastic collisions: \[ \text{Kinetic energy is not conserved} \]

Step 3: Evaluate each option.
(1) Kinetic energy is conserved → False (it is lost)
(2) Total energy is not conserved → False (total energy is always conserved)
(3) Linear momentum is not conserved → False (it is conserved)
(4) Bodies move as one after collision → True
(5) Bodies move separately → False

Step 4: Physical explanation.
During perfectly inelastic collision, part of kinetic energy is converted into heat, sound, or deformation energy, but bodies stick together and move jointly.

Step 5: Mathematical expression.
If masses \( m_1, m_2 \) stick together: \[ m_1u_1 + m_2u_2 = (m_1+m_2)v \] showing common velocity \( v \).

Step 6: Key observation.
The defining feature of perfectly inelastic collision is “sticking together,” not energy conservation.

Step 7: Final conclusion.
Hence, the correct statement is: \[ \boxed{\text{two bodies move as one body after collision}} \] Therefore, the correct option is \[ \boxed{(4)} \]