Suppose you have three different wires made of the same material. Wire 1 has len

Question

Suppose you have three different wires made of the same material.

Wire 1 has length L and cross-sectional area A.
Wire 2 has length 4L and cross-sectional area A.
Wire 3 has length L and cross-sectional area 4A.

When you hang a 2 kg mass on wire 1 it stretches by 1.2 mm, and when you hang 4 kg on wire 1 it stretches by 2.4 mm.

If you hang a 2 kg mass on wire 2, how much should it stretch? _____ mm.
If you hang a 2 kg mass on wire 3, how much should it stretch? _____ mm.

If you measure Young's modulus for all three wires, what should you find?

Young's modulus will be smaller for wire 2 than for wire 1, because wire 2 is longer.

Young's modulus will be larger for wire 3 than for wire 1, because wire 3 is thicker.

Young's modulus will be the same for wires 1, 2, and 3.

Explanation / Answer

since stress is same as first wire and Length is four times so extension will be four times

If you hang a 2 kg mass on wire 2, how much should it stretch? 4.8 mm.

since length is same and stress has become 1/4 time so extension becomes 1/4
If you hang a 2 kg mass on wire 3, how much should it stretch?0.8mm

B)

Young's modulus will be the same for wires 1, 2, and 3 ( its a metrial property)

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