Question

to answer this question, first click here to view the associated video. two objects have the same momentum. which of the following is true? i. the masses of the objects are equal. ii. the speeds of the objects are equal. iii. the velocities of the objects are equal. iv. the direction of motion of each object is the same. iii only i and ii iv only ii and iv i only ii and iii ii only

Explanation:

Step1: Recall the formula for momentum

Momentum \(p = mv\), where \(m\) is mass and \(v\) is velocity (a vector quantity).

Step2: Analyze each statement

• Statement I: If \(p_1=p_2\), \(m_1v_1 = m_2v_2\). Masses \(m_1\) and \(m_2\) are not necessarily equal. For example, if \(m_1 = 2\), \(v_1=3\) and \(m_2 = 3\), \(v_2 = 2\), \(p_1=p_2 = 6\) but \(m_1

eq m_2\).

• Statement II: Speed is the magnitude of velocity. From \(m_1v_1 = m_2v_2\), speeds \(|v_1|\) and \(|v_2|\) are not necessarily equal (due to different masses).
• Statement III: Velocity \(v\) is a vector. From \(m_1\vec{v}_1 = m_2\vec{v}_2\), velocities \(\vec{v}_1\) and \(\vec{v}_2\) are not necessarily equal (since masses can differ).
• Statement IV: Since momentum \(p = m\vec{v}\) is a vector, if \(p_1 = p_2\), the direction of \(\vec{v}_1\) and \(\vec{v}_2\) must be the same (because \(m>0\)).

Answer:

IV only