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

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" /> (A) 2Msinα (B) Msinα (C) 2Mtanα (D) Mcosα

Tardigrade Admin · Accepted Answer

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

Q. A spool of mass $M$ and radius $2 R$ 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

$2 M s in α$

$M s in α$

$2 Mt an α$

$M cos α$

Equilibrium of $m$ give
$T = m g$ ( $T$ = Tension in string)
Net torque about point of contact of the spool should be
zero. Hence,
$(2 R) (M g s in α) = TR$
or $2 M g s in α = m g$
or $m = 2 M s in α$

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

2Msinα

Msinα

2Mtanα

Mcosα