Two blocks of masses 5 kg and 10 kg are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal wire is 2 × 10 9 N m - 2 . If g = 10 m s - 2 , then what is the minimum radius of the wire which will not break

Step-by-step solution

This is Atwood's machine. Let the tension in the wire be T and acceleration of masses a . Then, T - 5 g = 5 a and 10 g - T = 10 a This gives a = 1 3 g and T ⁡ = 20 3 g = 200 3 N . Stress = T ⁡ area = 200 3 × 3 . 14 × r ⁡ 2 = 2 × 10 9               (given) Thus the minimum radius r should be r = 200 3 × 3 . 14 × 2 × 10 9 = 1 . 03 × 10 - 4   m ≈ 0 . 1   mm