Q. 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 $g = 10\ ms^{- 2}$ , then the maximum angular velocity of the stone will be
A) $4\ radians/sec$
B) $16\ radians/sec$
C) $\sqrt{21}\ radians/sec$
D) $2\ radians/sec$
Explanation
(a) Max. tension that string can bear $= 3.7\ kgwt = 37\ N$
Tension at lowest point of vertical loop $= mg + m\omega^{2}r$
$= 0.5 \times 10 + 0.5 \times \omega^{2} \times 4 = 5 + 2\omega^{2}$
$\therefore 37 = 5 + 2\omega^{2} \Rightarrow \omega = 4\ rad/s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.