If the ratio of lengths, radii and Young's Moduli of steel and brass wires in the figure are a , b and c respectively, then the corresponding ratio of increase in their lengths would be

Step-by-step solution

Let L_s, r_s, Y_s be the length, radius, and Young's modulus of the steel wire, and L_b, r_b, Y_b be those of the brass wire. Given ratios are L_s L_b = a , r_s r_b = b , and Y_s Y_b = c . The tension in the steel wire is T_s = 2Mg (supporting the 2M mass). The tension in the brass wire is T_b = (M + 2M)g = 3Mg (supporting both masses). The elongation L is given by L = TL AY = TL r^2 Y . The ratio of increase in lengths is L_s L_b = T_s L_s r_s^2 Y_s r_b^2 Y_b T_b L_b = ( T_s T_b ) ( L_s L_b ) ( r_b r_s )^2 ( Y_b Y