Small smooth spheres A and B, of equal radii and of masses 5 kg and 3 kg respectively, lie on a smooth horizontal plane. Initially B is at rest and A is moving towards B with speed 8.5ms⁻¹. The spheres collide and after the collision A continues to move in the same direction but with a quarter of the speed of B.

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

1. [M1] Conservation of momentum; 3 terms; allow M1 if speed of A after collision is 1/4 × 8.5. Allow 5×8.5=5X+3Y where |X and Y are different which may be seen by later work. If |X| and Y are subsequently used as being equal then M0.
2. [A1] 5×8.5=5×0.25v+3v OE e.g. 5×8.5=5V+3×4V
3. [A1] Speed of B = 10ms⁻¹ Do not award if 10 from using mgv, maximum 2/3 -10 is A0 as speed required not velocity
4. [M1] Attempt at any of the 3 terms for KE, using their 10ms⁻¹ Not ½x(5+3)×8.5², not ½x(5+3)×2.5² not ½x(5+3)×10² unless |X| = |Y| seen
5. [A1] KE before = ½×5×8.5² [=180.625] KE after = ½×5×2.5² + ½×3×10² [=15.625+150=165.625]
6. [A1] KE loss [=180.625-165.625]=15 J Accept -15, AWRT ±15.0