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A spool of inner radius $r$ and outer radius $R$ ($r < R$) rests on a rough horizontal floor. A thread is pulled **horizontally** off the **bottom** of the inner shaft. The spool:
AAlways rolls toward the puller
BAlways rolls away from the puller
CRolls toward the puller (thread is below the contact point of effective axis)
DDepends on coefficient of friction
Answer & Solution
Correct answer: C. Rolls toward the puller (thread is below the contact point of effective axis)
Take torque about the **contact point** (instantaneous axis). Pull force acts horizontally at height $r$ above the floor, so its moment arm about the contact point is $r$ — the torque rotates the spool such that it rolls TOWARD the puller, taking up the thread. Counter-intuitive but well-tested JEE Adv result. (Pulling above the centre would reverse direction.)
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