Two blocks of mass \(m\) and \(2m\) are connected with a string that goes over a pulley of mass \(m\). The pulley has radius \(r\) and moment of inertia \(I=\dfrac{mr^2}{2}\).
(a) Show that the acceleration of the blocks is given by \(a=\dfrac{2g}{7}\).
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(b) Suggest whether the angular momentum of the pulley-blocks system is conserved.
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Most-appropriate topic codes (IBDP Physics HL 2025):
(a) Correct Answer: \(\boxed{a=\dfrac{2g}{7}}\)
Applying Newton’s second law to the two blocks,
\(2mg-T_2=2ma\)
\(T_1-mg=ma\)
For the pulley,
\((T_2-T_1)r=I\alpha\)
Using \(I=\dfrac{mr^2}{2}\) and \(\alpha=\dfrac{a}{r}\),
\(T_2-T_1=\dfrac{ma}{2}\)
Combining the three equations gives
\(mg-\dfrac{ma}{2}=3ma\)
Hence,
\( a=\frac{2g}{7} \)
(b) Correct Answer: \(\boxed{\text{No}}\)
The angular momentum of the pulley-blocks system is not conserved because there is a non-zero external torque acting on the system due to gravity.
