A-LevelMathematicsMechanics9709/41 · May/June 2021 · Q26 Marks

Two particles A and B have masses mkg and 0.1 kg respectively, where m > 0.1. 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 it. Both particles are at a height of 0.9 m above horizontal ground [Figure 2.1]. The system is released from rest, and while both particles are in motion the tension in the string is 1.5 N. Particle B does not reach the pulley.

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Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

[M1] T-0.1g = 0.1a Apply Newton's 2nd law to either the 0.1 kg particle, the m kg particle or to the system, correct number of terms
[A1] mg-T = ma Two correct equations
[M1] mg-0.1g = (m +0.1)a From 2 equations with the correct number of relevant terms
[A1] [a=5]
[M1] v²=0+2×5×0.9 Use of v² = u² + 2as with u=0, s=0.9 and their a≠±g
[A1] v=3 ms⁻¹ FT on √1.8a

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