A string of area of cross-section 4 mm 2 and length 0 . 5 is connected with a rigid body of mass 2 kg . The body is rotated in a vertical circular path of radius 0 . 5 m . The body acquires a speed of 5 m s - 1 at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is _____ × 10 - 5 . (Use Young's modulus 10 11 N m - 2 and g = 10 m s - 2 )

Step-by-step solution

Given here, A = 4   mm 2 , l = 0 . 5   m , m = 2   kg and v b = 5   m   s - 1 . Tension at the bottom of the circular motion is given by T = m g + m v b 2 R Using Young's modulus, we have Strain produced in the string when the body is at the bottom of the circle is ∆ l l = T A Y = m g + m v b 2 l A Y = 20 + 2 5 2 0 . 5 3 × 10 - 6 × 10 11 = 30 × 10 - 5