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Q.

Two steel wires of same length but radii r and 2r are connected together end to end and tied to a wall as shown.The force stretches the combination by 10 mm. How far does the midpoint A move (in mm)?

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answer is 8.

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Detailed Solution

FA1=YΔl1l⇒Δl1=FlA1yFA2=YΔl2l⇒Δl2=FlA2y=Fl4A1y∴∆l1=4∆l2 Δl1+Δl2=10mmFlA1Y+Fl4A1Y=10mm⇒FlA1Y=8mmmid point will be moved because ofexpansion in the  upper part of the rod
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