A wire of cross sectional area A, modulus of elasticity 2 10¹¹ Nm ⁻² and length 2 ~m is stretched between two vertical rigid supports. When a mass of 2 ~kg is suspended at the middle it sags lower from its original position making angle = 1 100 radian on the points of support. The value of A is _______ 10⁻⁴ ~m ^2 (consider x

Step-by-step solution

In vertical direction 2 ~T =20 using small angle approximation = aligned & = 1 100 & T = 10 & T =1000 ~N aligned array ll Change in length L =2 x ^2+ L ^2 -2 ~L =2 ~L [1+ x ^2 2 ~L ^2 -1 ] L = x ^2 ~L array Modulus of elasticity = stress strain aligned & 2 10¹¹= 10^3 ~A x ^2 ~L 2 ~L & A =1 10⁻⁴ ~m ^2 aligned