Two wires as shown in the figure below, made of steel and have breaking stress of 12 10^8 N/m ^2 . Area of cross-section of upper wire is 0.008 cm ^2 and of lower wire is 0.004 cm ^2 . The maximum mass that can be added to pan without breaking any wire is _____ kg. (take g = 10 m/s ^2 )

Step-by-step solution

Let the maximum mass that can be added to the pan be m . The breaking stress for both wires is _ max = 12 10^8 N/m ^2 . For the upper wire: Area of cross-section, A_u = 0.008 cm ^2 = 8 10⁻⁷ m ^2 Maximum tension the upper wire can withstand is: T_ u,max = _ max A_u = (12 10^8) (8 10⁻⁷) = 960 N The total mass supported by the upper wire is (30 + 10 + m) = (40 + m) kg . Tension in the upper wire, T_u = (40 + m)g = (40 + m) 10 To avoid breaking the upper wire: (40 + m) 10 960 40 + m 96 m 56 kg For the lower wire: Area