A stone of mass 40 g is tied to a light inextensible string of length 50 cm and whirled in a vertical circle at the rate of 30 revolutions per minute. The tension in the string when it is at the lowest point of the circle is (Take gravitational acceleration, g = 10 , m/s ^2 and ^2 = 10 )

Step-by-step solution

Mass of the stone, m = 40 g = 0.04 kg Length of the string, r = 50 cm = 0.5 m Frequency of revolution, f = 30 rev/min = 30 60 rev/s = 0.5 rev/s Angular velocity, = 2 f = 2 0.5 = rad/s At the lowest point of the vertical circle, the net force towards the center provides the necessary centripetal force. The forces acting on the stone are tension T upwards and weight mg downwards. T - mg = m ^2 r T = m(g + ^2 r) Substituting the given values and using ^2 = 10 : T = 0.04(10 + ^2 0.5) T = 0.04(10 + 10 0.5) T = 0.04(10 +