Two steel wires of radii r and 2 r are connected together end to end and tied to a wall as shown. The force stretches the combination by (27/4) mm. How far (in mm ) does the junction point A move?

Question

Two steel wires of radii r and 2 r are connected together end to end and tied to a wall as shown. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/3cfb1fe4f3a1c5f7e7aab2e404e9842d-.png" /> The force stretches the combination by (27/4) mm. How far (in mm ) does the junction point A move? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/e58f9d2dd20da0ffccb969463a33ad7a-.png" /> (F/A1)=Y (Δ l1/2 L) (F/A2)=Y (Δ l2/L) Δ l1+Δ l2=(27/4) mm (2 F L/A1 Y)+(F L/4 A1 Y)=(27/4) mm

Q. Two steel wires of radii $r$ and $2 r$ are connected together end to end and tied to a wall as shown.

The force stretches the combination by $\frac{27}{4} mm$ . How far (in $mm$ ) does the junction point $A$ move?

$\frac{F}{A _{1}} = Y \frac{Δ l _{1}}{2 L}$
$\frac{F}{A _{2}} = Y \frac{Δ l _{2}}{L}$
$Δ l_{1} + Δ l_{2} = \frac{27}{4} mm$
$\frac{2 F L}{A _{1} Y} + \frac{F L}{4 A _{1} Y} = \frac{27}{4} mm$

Q. Two steel wires of radii r and 2r are connected together end to end and tied to a wall as shown. The force stretches the combination by 427​mm. How far (in mm ) does the junction point A move?

A1​F​=Y2LΔl1​​ A2​F​=YLΔl2​​ Δl1​+Δl2​=427​mm A1​Y2FL​+4A1​YFL​=427​mm

Q. Two steel wires of radii $r$ and $2 r$ are connected together end to end and tied to a wall as shown.

The force stretches the combination by $\frac{27}{4} mm$ . How far (in $mm$ ) does the junction point $A$ move?

$\frac{F}{A _{1}} = Y \frac{Δ l _{1}}{2 L}$
$\frac{F}{A _{2}} = Y \frac{Δ l _{2}}{L}$
$Δ l_{1} + Δ l_{2} = \frac{27}{4} mm$
$\frac{2 F L}{A _{1} Y} + \frac{F L}{4 A _{1} Y} = \frac{27}{4} mm$