9. The diagram below shows an object \(A\), of mass \(2 m \mathrm {~kg}\), lying on a horizontal table. It is connected to another object \(B\), of mass \(m \mathrm {~kg}\), by a light inextensible string, which passes over a smooth pulley \(P\), fixed at the edge of the table. Initially, object \(A\) is held at rest so that object \(B\) hangs freely with the string taut.
\includegraphics[max width=\textwidth, alt={}, center]{d9ef2033-bf8b-4aec-bc88-34dbc8b9c208-20_589_871_593_605}
Object \(A\) is then released.
- When object \(B\) has moved downwards a vertical distance of 0.4 m , its speed is \(1.2 \mathrm {~ms} ^ { - 1 }\). Use a formula for motion in a straight line with constant acceleration to show that the magnitude of the acceleration of \(B\) is \(1.8 \mathrm {~ms} ^ { - 2 }\).
- During the motion, object \(A\) experiences a constant resistive force of 22 N . Find the value of \(m\) and hence determine the tension in the string.
- What assumption did the word 'inextensible' in the description of the string enable you to make in your solution?
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