A 100 g sphere is moving at a speed of 20 m/s and collides with another. sphere of mass 50 g. If the second sphere was at rest prior to the collision and the first sphere comes at rest immediately after the collision, considering the collision to be elastic, the speed of the second sphere would be

The correct answer is 40 m/s.

Key Points

• In an elastic collision between two spheres, both momentum and kinetic energy are conserved.
• The conservation of momentum can be expressed as:
  • m₁*v_1i ​ + m₂*v_2i  = m₁*v_1f ​ + m₂*v_2f ​
    • where:
    • m₁ and m₂ ​ are the masses of the first and second spheres, respectively,
    • v_1i and v_2i are their initial velocities,
    • v_{1f ​} and v_2f ​are their final velocities.
• Since the second sphere is initially at rest (v_2i ​= 0) and the first sphere comes to rest (v_1f​ = 0), the momentum conservation equation simplifies to: 
• m1*v1i ​ = m2*v2f
• Now, let's substitute the given values:
• 100 g*20 m/s = 50 g*v_2f
• Solving for v2f ​:
• v_2f ​ = 40m/s
• Therefore, the speed of the second sphere after the collision is 40 m/s.