Question

1. what happens in a perfectly elastic collision when two objects of the same mass are with moving before the collision?

the velocity in both objects would stay the same.
the velocity of both objects would be zero.
the velocity for both objects would increase.
they would exchange velocities.

Explanation:

Step1: Recall the concept of a perfectly elastic collision

In a perfectly elastic collision between two objects of the same mass, the velocities of the objects are exchanged. This is based on the conservation of momentum ($m_1u_1 + m_2u_2=m_1v_1 + m_2v_2$) and conservation of kinetic energy ($\frac{1}{2}m_1u_1^{2}+\frac{1}{2}m_2u_2^{2}=\frac{1}{2}m_1v_1^{2}+\frac{1}{2}m_2v_2^{2}$). When $m_1 = m_2$, solving these equations gives $v_1=u_2$ and $v_2 = u_1$.

Step2: Analyze each option

• Option "The velocity in both objects would stay the same": Incorrect. In a collision, velocities change.
• Option "The velocity of both objects would be zero": Incorrect. This is the case for a perfectly inelastic collision (if they stick together) but not for a perfectly elastic collision.
• Option "The velocity for both objects would increase": Incorrect. There is no reason for velocities to increase as kinetic energy is conserved (not increased) in a perfectly elastic collision.
• Option "They would exchange velocities": Correct. As per the equations of conservation of momentum and kinetic energy for equal - mass objects in a perfectly elastic collision.

Answer:

They would exchange velocities.