A weightless thread can bear tension up to 3.7 kg wt. A stone of mass 500 gram is tied to it and revolved in circular path of radius 4 m in vertical plane. Maximum angular velocity of the stone will b

Question

A weightless thread can bear tension up to 3.7 kg wt. A stone of mass 500 gram is tied to it and revolved in circular path of radius 4 m in vertical plane. Maximum angular velocity of the stone will be (acceleration due to gravity, g = 10 m / s 2 )

TestHub · Accepted Answer

Maximum tension in a vertical circle occurs at the lowest point of the path.

$T_{max} = m ω^{2} r + m g$

Given $T_{max} = 3.7 kg wt = 3.7 \times 10 = 37 N$ , $m = 500 g = 0.5 kg$ , $r = 4 m$ , and $g = 10 m/s^{2}$ .

Substituting the values into the equation:

$37 = 0.5 \times ω^{2} \times 4 + 0.5 \times 10$

$37 = 2 ω^{2} + 5$

$2 ω^{2} = 32$

$ω^{2} = 16$

$ω = 4 rad/s$

Answer: $4 rad / s$

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