A-LevelMathematicsMechanics9709/42 · Feb/Mar 2025 · Q47 Marks

Two particles A and B have masses 0.3kg and 0.1kg respectively. The particles are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley, and the particles hang vertically below the pulley. Both particles are initially at a height of xm above horizontal ground (see diagram). The system is released from rest. [Figure X.X]

(a)Find the tension in the string and the acceleration of the particles.[4]
(b)During the subsequent motion, B does not reach the pulley. When A reaches the ground, it comes to rest. Given that the greatest height of B above the ground is 1.2m, find the value of x.[3]

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Mark scheme

Marking points from the official mark scheme (Feb/Mar 2025). The mark or mark type is shown in brackets.

*M1 Allow g missing. Correct number of terms. Allow sign errors.
A1 Any 2 consistent equations, e.g. allow -a for a if consistent. Must be same T if individual particle equations.
DM1 From equation(s) with correct number of relevant terms. Allow g missing. Must get to ‘T =' or ‘a ='. If no solving seen, must be correct answers for their equations for this mark.
A1 Allow acceleration = -5 m s-2.
*M1 For use of constant acceleration to find v² or v in terms of x. Using |their a|, a≠±g.
DM1 For use of v² =u² + 2as to get an equation in x only. Allow a=±g.
A1 OE

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