Question

A rigid bar of mass 15 kg is supported symmetrically by three wires each 2.0 m long. Those at each end are of copper and the middle one is of Iron. Determine the ratios of their diameters if each is to have the same tension.

Answer 1

Since the rigid bar is supported symmetrically by three wires each of length 2 m, the extension is same in all the three wires. Thus strain is same.

Y 

∴ Y α\(\frac{1}{d^2}\) 

Y_i = Young’s modulus of Iron

d_i = diameter of iron wire

Y_c = Young’s modulus of copper

d_c = diameter of copper wire.

Y_i = 190 × 10⁹ N m^-2

Y_c = 110 × 10⁹ N m^-2