A stone of mass 0.25 kg tied to the end of a string is whirled round i

1.	A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N?
Answer» Mass of the stone, m = 0.25 kg Radius of the circle, r = 1.5 m Number of revolution per second, n = 40/60 = (2/3)rps Angular velocity, ω = / = 2 ………………….(i) The centripetal force for the stone is provided by the tension T, in the string, i.e., T = F_Centripetal = mv²/r = mrω² = mr(2πn)² = 6.57 N Maximum tension in the string, T_max = 200 N T_max = mv²_max/r v_max = √T_max x r/m = √200 x 1.5/0.25 = √1200 = 34.64 m/s Therefore, the maximum speed of the stone is 34.64 m/s.

A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N?

Answer»

Mass of the stone, m = 0.25 kg

Radius of the circle, r = 1.5 m

Number of revolution per second, n = 40/60 = (2/3)rps

Angular velocity, ω = / = 2 ………………….(i)

The centripetal force for the stone is provided by the tension T, in the string, i.e.,

T = F_Centripetal

= mv²/r = mrω² = mr(2πn)²

= 6.57 N

Maximum tension in the string, T_max = 200 N

T_max = mv²_max/r

v_max = √T_max x r/m

= √200 x 1.5/0.25

= √1200 = 34.64 m/s

Therefore, the maximum speed of the stone is 34.64 m/s.