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the chart lists the masses of four balls that have the same momentum. w…

Question

the chart lists the masses of four balls that have the same momentum. which correctly compares two of the balls? the green ball has a lower velocity than the purple ball. the red ball has a greater velocity than the purple ball. the yellow ball has a higher velocity than the green ball. the red ball has a greater velocity than the green ball.

Explanation:

Step1: Recall momentum formula

Momentum \(p = mv\), where \(m\) is mass and \(v\) is velocity. Given \(p\) is the same for all balls, \(v=\frac{p}{m}\), so velocity is inversely - proportional to mass.

Step2: Analyze mass - velocity relationship for each option

  • Option 1: Mass of green ball \(m_{g}=0.5\) kg, mass of purple ball \(m_{p}=1.7\) kg. Since \(m_{g}v_{p}\), so this option is wrong.
  • Option 2: Mass of red ball \(m_{r}=1.2\) kg, mass of purple ball \(m_{p}=1.7\) kg. Since \(m_{r}v_{p}\), this option is correct.
  • Option 3: Mass of yellow ball \(m_{y}=0.9\) kg, mass of green ball \(m_{g}=0.5\) kg. Since \(m_{y}>m_{g}\), then \(v_{y}
  • Option 4: Mass of red ball \(m_{r}=1.2\) kg, mass of green ball \(m_{g}=0.5\) kg. Since \(m_{r}>m_{g}\), then \(v_{r}

Answer:

The red ball has a greater velocity than the purple ball.