Question

When two identical balls are moving with equal speeds in opposite directions, which of the following is true for the system of two bodies?

• A. Momentum is zero, kinetic energy is zero
• B. Momentum is not zero, kinetic energy is zero
• C. Momentum is zero, kinetic energy not zero
• D. Momentum is not zero, kinetic energy is not zero

Answer 1

The correct option is C Momentum is zero, kinetic energy not zero

Let mass of the balls be $m_1$ and $m_2$ and their velocities $v_1$ and $v_2$ respectively.

$m_1=m_2,v_1=-v_2$

Total momentum,

${\overrightarrow{p}}_{total}=m_1\overrightarrow{v_1}+m_2\overrightarrow{u_2}$

${\overrightarrow{p}}_{total}=m_1\overrightarrow{v_1}-m_1\overrightarrow{v_1}=0$

Total kinetic energy,

$E=\frac{1}{2}{m}_1{v}_1^2+\frac{1}{2}{m}_2{v}_2^2$

$E=\frac{1}{2}{m}_1{v}_1^2+\frac{1}{2}{m}_1{v}_1^2=m_1{v}_1^2$

So momentum is zero, kinetic energy is not zero.