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Question: A weightless thread can support tension upto 30 N. A stone of mass 0.5 kg is tied to it and is revol...

A weightless thread can support tension upto 30 N. A stone of mass 0.5 kg is tied to it and is revolved in a circular path of radius 2 m in a vertical plane. If g=10 m/s2g = 10 \mathrm {~m} / \mathrm { s } ^ { 2 } , then the maximum angular velocity of the stone will be

A

5rad/s5 \mathrm { rad } / \mathrm { s }

B

30rad/s\sqrt { 30 } \mathrm { rad } / \mathrm { s }

C

60rad/s\sqrt { 60 } \mathrm { rad } / \mathrm { s }

D

10rad/s10 \mathrm { rad } / \mathrm { s }

Answer

5rad/s5 \mathrm { rad } / \mathrm { s }

Explanation

Solution

Tmax⁡=mωmax⁡2r+mgT _ { \max } = m \omega _ { \max } ^ { 2 } r + m g ⇒ Tmax⁡m=ω2r+g\frac { T _ { \max } } { m } = \omega ^ { 2 } r + g

⇒ 300.5−10=ωmax⁡2r\frac { 30 } { 0.5 } - 10 = \omega _ { \max } ^ { 2 } r ⇒ ωmax⁡=50r=502=5rad/s\omega _ { \max } = \sqrt { \frac { 50 } { r } } = \sqrt { \frac { 50 } { 2 } } = 5 \mathrm { rad } / \mathrm { s }