We have two wires W1 and W2. Both are made of same material and have the same length. The radius of cross-section W2 is twice that of W1. Same load is suspended from both of them. If the strain in W1 be 4, then that in W2 will be

Question

We have two wires W1 and W2. Both are made of same material and have the same length. The radius of cross-section W2 is twice that of W1. Same load is suspended from both of them. If the strain in W1 be 4, then that in W2 will be (A) 1 (B) 2 (C) 4 (D) 8

Tardigrade Admin · Accepted Answer

using, ( F / A )= Y (Δ l 1/ l 1) ( F /π r 2)= Y (4) longrightarrow for W 1 ⇒ F =4 π r 2 Y for W 2 longrightarrow (4 π r 2 Y /4 π r 2)= Y (Δ l 2/ l 2) ⇒ (Δ l 2/ l 2)=1

Q. We have two wires $W_{1}$ and $W_{2}$ . Both are made of same material and have the same length. The radius of cross-section $W_{2}$ is twice that of $W_{1}$ . Same load is suspended from both of them. If the strain in $W_{1}$ be 4, then that in $W_{2}$ will be

1

2

4

8

using, $\frac{F}{A} = Y \frac{Δ l _{1}}{l _{1}}$
$\frac{F}{π r ^{2}} = Y (4) ⟶$ for $W_{1}$
$\Rightarrow F = 4 π r^{2} Y$
for $W_{2} ⟶$
$\frac{4 π r ^{2} Y}{4 π r ^{2}} = Y \frac{Δ l _{2}}{l _{2}}$
$\Rightarrow \frac{Δ l _{2}}{l _{2}} = 1$

Q. We have two wires W1​ and W2​. Both are made of same material and have the same length. The radius of cross-section W2​ is twice that of W1​. Same load is suspended from both of them. If the strain in W1​ be 4, then that in W2​ will be

1

2

4

8

using, AF​=Yl1​Δl1​​ πr2F​=Y(4)⟶ for W1​ ⇒F=4πr2Y for W2​⟶ 4πr24πr2Y​=Yl2​Δl2​​ ⇒l2​Δl2​​=1

Q. We have two wires $W_{1}$ and $W_{2}$ . Both are made of same material and have the same length. The radius of cross-section $W_{2}$ is twice that of $W_{1}$ . Same load is suspended from both of them. If the strain in $W_{1}$ be 4, then that in $W_{2}$ will be

using, $\frac{F}{A} = Y \frac{Δ l _{1}}{l _{1}}$
$\frac{F}{π r ^{2}} = Y (4) ⟶$ for $W_{1}$
$\Rightarrow F = 4 π r^{2} Y$
for $W_{2} ⟶$
$\frac{4 π r ^{2} Y}{4 π r ^{2}} = Y \frac{Δ l _{2}}{l _{2}}$
$\Rightarrow \frac{Δ l _{2}}{l _{2}} = 1$