A stone of mass 1 . 3   kg is being rotated in a horizontal plane as a conical pendulum with the help of a 140   cm long aluminium wire of cross-sectional area 1   mm 2 . The wire makes an angle θ = 75 ° with the vertical. What is the increment in the length (in mm ) of the wire? [Young's modulus of aluminium Y Al = 7 × 10 10   N m -2 , sin 75 ° ≈ 0 . 97 , cos 75

Step-by-step solution

The figure below shows the stone being rotated as a conical pendulum such that the wire makes an angle of 75 ° with the vertical. Let us assume that the radius OA of the circle is equal to r For vertical equilibrium of the stone T cos 75 ° = M g T = M g cos 75 ° The elongation in the wire is ∆ L = T L A Y = M g L A Y cos 75 ° ⇒ ∆ L = 1 . 3 × 10 × 1 . 4 10 - 6 × 7 × 10 10 × 0 . 26 = 10 - 3   m = 1   mm