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\includegraphics[max width=\textwidth, alt={}, center]{6853f050-45ed-4a76-b450-648d8ac91468-2_560_591_1663_776} The diagram shows the vertical cross-section of a surface. \(A\) and \(B\) are two points on the cross-section, and \(A\) is 5 m higher than \(B\). A particle of mass 0.35 kg passes through \(A\) with speed \(7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), moving on the surface towards \(B\).

1. Assuming that there is no resistance to motion, find the speed with which the particle reaches \(B\).
2. Assuming instead that there is a resistance to motion, and that the particle reaches \(B\) with speed \(11 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), find the work done against this resistance as the particle moves from \(A\) to \(B\). A ring of mass 4 kg is threaded on a fixed rough vertical rod. A light string is attached to the ring, and is pulled with a force of magnitude \(T \mathrm {~N}\) acting at an angle of \(60 ^ { \circ }\) to the downward vertical (see diagram). The ring is in equilibrium.