Question:
A mass 'm' is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release ?
A mass 'm' is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release ?
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A hollow cylinder has \(I=mR^2\); write the torque equation and the equation of motion of the hanging mass.
Updated On: Nov 11, 2026
- \(\frac{2g}{3}\)
- \(\frac{g}{2}\)
- \(\frac{5g}{6}\)
- g
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The Correct Option is B
Solution and Explanation
For the falling mass: \(mg-T=ma\).
For the hollow cylinder (\(I=mR^2\)) about its axis: \(TR=I\alpha=mR^2\cdot\frac aR\Rightarrow T=ma\).
Adding: \(mg=2ma\Rightarrow a=\frac g2\).
Answer: (2) \(\frac g2\)
For the hollow cylinder (\(I=mR^2\)) about its axis: \(TR=I\alpha=mR^2\cdot\frac aR\Rightarrow T=ma\).
Adding: \(mg=2ma\Rightarrow a=\frac g2\).
Answer: (2) \(\frac g2\)
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