Question

Particle A has half the mass and twice the speed of particle B. Is the momentum P_A less than, greater than, or equal to P_B? Explain.

Short answer

The momentum ofP_Ais greater than the momentum ofP_B.

Step-by-step solution

Given information

It is given that the mass of particle A is half the mass of B and Particle A has double the speed.

Explanation

In classical theory, they are deemed equal. While in the theory of relativity,

$\frac{p_a}{p_b}=\frac{{\gamma }_{pa}\left(0.5m_b\right)\left(2u_b\right)}{{\gamma }_{pb}{m}_b{u}_b}=\frac{{\gamma }_{pa}}{{\gamma }_{pb}}>1$

As $\frac{p_a}{p_b}>1$

i.e$p_a>p_b$

Therefore,

The momentum ofP_Ais greater than the momentum ofP_B.