A weightless thread can bear tension upto $3.7\, kg wt.$ A stone of mass $500\, gms$ is tied to it and revolved in a circular path of radius $4 m$ in a vertical plane. If $g = 10\,m{s^{ - 2}}$, then the maximum angular velocity of the stone will be ........ $rad/\sec$
A weightless thread can bear tension upto $3.7\, kg wt.$ A stone of mass $500\, gms$ is tied to it and revolved in a circular path of radius $4 m$ in a vertical plane. If $g = 10\,m{s^{ - 2}}$, then the maximum angular velocity of the stone will be ........ $rad/\sec$
$4 $
$16$
$\sqrt {21} $
$2$
A weightless thread can bear tension upto $3.7\, kg wt.$ A stone of mass $500\, gms$ is tied to it and revolved in a circular path of radius $4 m$ in a vertical plane. If $g = 10\,m{s^{ - 2}}$, then the maximum angular velocity of the stone will be ........ $rad/\sec$
Max. tension that string can bear = $3.7 \,kgwt = 37\,N$
Tension at lowest point of vertical ${\rm{loop}} = mg + m{\omega ^2}r$
= $0.5 \times 10 + 0.5 \times {\omega^2}\times 4 = 5 + 2{\omega ^2}$
$37 = 5 + 2$ ${\omega^2}$
$⇒$ $\omega= 4\, rad/s.$
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