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  4. A spool of mass M and radius 2R lies on an inclined plane as shown in figure. A light thread is wound around the connecting tube of the spool and its free end carries a weight of mass m . The value of m so that system is in equilibrium is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-afetmnwmoory.png />

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Q. A spool of mass $M$ and radius $2R$ lies on an inclined plane as shown in figure. A light thread is wound around the connecting tube of the spool and its free end carries a weight of mass $m$ . The value of $m$ so that system is in equilibrium is

Question

NTA AbhyasNTA Abhyas 2020System of Particles and Rotational Motion

Solution:

Equilibrium of $m$ give
$T=mg$ ( $T$ = Tension in string)
Net torque about point of contact of the spool should be
zero. Hence,
$\left(\right.2R\left.\right)\left(\right.Mgsinα\left.\right) \, = \, TR$
or $2Mgsinα \, = \, mg$
or $m \, = \, 2Msinα$