91Ó°ÊÓ

A particle of weight \(W\) is attached by two light inextensible strings cach of length \(a\) to two fixed points distant \(a\) apart in a horizontal line. Write down the tension in either string. One of the strings is now replaced by an elastic string of the same natural length, and it is found that in the new position of equilibrium this string has stretched to a length \(5 a / 4\). Prove that the modulus of elasticity of this string is \(7 W / \sqrt{39}\), and show that the tension in the other string has been increased in the ratio \(5: \sqrt{13}\). (U of L)

A particle is hanging in equilibrium at one end of an elastic string whose other end is fixed. Find the distance between the particle and the fixed end: (a) the particle weighs \(10 \mathrm{~N}\), (b) the modulus of elasticity is \(8 \mathrm{~N}\), (c) the natural length of the string is \(2 \mathrm{~m}\).