A metal wire of length 0 . 5 m and cross-sectional area 10 - 4 m 2 has breaking stress 5 × 10 8 N m - 2 . A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _____ m s - 1 .

Step-by-step solution

Here in horizontal circular motion, the only centripetal force is tension. So, T = m ω 2 r = m v 2 l = 10 × v 2 0 . 5 = 20 v 2 Now, T max = Breaking stress × Area ⇒ 20 v 2 = 5 × 10 8 × 10 - 4 ⇒ 20 v 2 = 5 × 10 4 Thus, the maximum linear velocity of block is v = 1 4 10 4 = 50   m   s - 1