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 )

Step-by-step solution

Maximum angular velocity occurs at the lowest point where tension is greatest due to the combined effect of weight and centripetal force. The tension formula at the lowest point is T = mg + m ^2 r . Given: T_ max = 3.7 , kg wt = 37 , N , m = 0.5 , kg , r = 4 , m , g = 10 , m/s ^2 . Substituting known values: 37 = 0.5 10 + 0.5 ^2 4 37 = 5 + 2 ^2 32 = 2 ^2 ^2 = 16 The angular velocity is = 4 , rad/s . Answer: B