A sphere of mass 3 kg strikes at velocity of 5 m/s to another sphere of mass 2 kg, which is at rest. What would be their common velocity, if they move together after collision?

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Question

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BHEL Engineer Trainee Mechanical 24 Aug 2023 Official Paper

Answer 1

Concept:

When two bodies collide and move together after the collision, the principle of conservation of momentum is applied.

The equation for conservation of momentum is given by:

\( m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_f \)

Where:

\( m_1 = 3 \) kg (mass of first sphere)
\( v_1 = 5 \) m/s (velocity of first sphere before collision)
\( m_2 = 2 \) kg (mass of second sphere)
\( v_2 = 0 \) m/s (velocity of second sphere before collision, since it is at rest)
\( v_f \) is the common velocity after collision

Calculation:

Applying the conservation of momentum equation:

\( (3 \times 5) + (2 \times 0) = (3 + 2) v_f \)

\( 15 = 5 v_f \)

\( v_f = \frac{15}{5} = 3 \) m/s