smc-1060-40-Pulleys (no air resistance)

A light string passes over a smooth pulley. Attached to the ends of the string are masses of 9 kg and 5 kg , as shown.

The acceleration due to gravity is \(g\) m s\(^{-2}\).

What is the acceleration of the 9 kg mass?

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\(A\)

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\(\text{Net force on 9 kg mass}\ = 9g-T\ \text{(down)}\)

\(\text{Net force on 5 kg mass}\ = 5g-T\ \text{(up)}\)

\(\text{Using}\ \ F=ma: \)

\(9 \times a\)	\(=9g-T\ …\ (1)\)
\(5 \times a\)	\(=-(5g-T)\ …\ (2) \)

\(\text{Adding (1) + (2):}\)

\(14a\)	\(=4g\)
\(a\)	\(=\dfrac{2}{7}g\)

\(\Rightarrow A\)