Question

A body of mass 1000 kg is moving horizontally with a velocity of 6 m/s. If 200 kg extra mass is added, the final velocity (in m/s) is:

• A. 5 m/s
• B. 4 m/s
• C. 2 m/s
• D. 6 m/s

Answer 1

The Correct Option is A

To resolve this issue, the principle of conservation of momentum will be employed. This principle states that the aggregate momentum of a closed system, one unaffected by external forces, remains constant.

Step-by-step Solution:

1. Compute the initial momentum of the object:

The initial mass of the object is \(1000 \, \text{kg}\) and its initial velocity is \(6 \, \text{m/s}\). The initial momentum (\(p_{\text{initial}}\)) is calculated as:

\(p_{\text{initial}} = m_{\text{initial}} \times v_{\text{initial}} = 1000 \times 6 = 6000 \, \text{kg m/s}\)

1. Compute the final momentum of the system:

Following the addition of 200 kg, the total mass increases to \(1000 + 200 = 1200 \, \text{kg}\). Let the final velocity be denoted as \(v_{\text{final}}\). The final momentum (\(p_{\text{final}}\)) is represented by:

\(p_{\text{final}} = m_{\text{final}} \times v_{\text{final}} = 1200 \times v_{\text{final}}\)

1. Apply the conservation of momentum:

Based on the conservation of momentum:

\(p_{\text{initial}} = p_{\text{final}}\)

\(6000 = 1200 \times v_{\text{final}}\)

1. Determine \(v_{\text{final}}\):

The equation is rearranged to solve for \(v_{\text{final}}\):

\(v_{\text{final}} = \frac{6000}{1200} = 5 \, \text{m/s}\)

Consequently, the final velocity of the object subsequent to the addition of 200 kg of mass is 5 m/s.

Conclusion: The correct result is \(5 \, \text{m/s}\), corresponding to option

5 m/s

. This outcome validates option

5 m/s

as the correct selection.