Two wires, 1 and 2, made of the same material and having equal initial lengths, are connected in series and suspended vertically from a rigid support. Wire 1 is at the top and wire 2 is at the bottom. A block of mass m is attached between the two wires, and another block of mass 3m is attached to the lower end of wire 2. If the ratio of the elongation in wire 1 to the elongation in wire 2 is 3 , the ratio of the cros

Step-by-step solution

The tension in wire 2 (the bottom wire) is due to the mass 3m suspended below it: T₂ = 3mg The tension in wire 1 (the top wire) is due to both masses suspended below it: T₁ = mg + 3mg = 4mg According to Hooke's law, the elongation L of a wire is given by: L = TL AY = TL r^2 Y Since both wires have the same initial length L and are made of the same material (same Young's modulus Y ), the elongation is proportional to T r^2 . Taking the ratio of the elongations: L₁ L₂ = ( T₁ T₂ ) ( r₂ r₁ )^2 Substitute the given valu