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 0 = 75° with the vertical. What is the increment in the length (in mm) of the wire? [Young's modulus of aluminium Y Al = 7 x 10 10 N m -2 , sin 75°
0. 97, cos 75°
0. 26, g = 10 m s -2 ]
Text Solution
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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°=Mg

The elongation in the wire is


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