The length of a metal wire is l1 when the tension in it is T1 and is l2 when the tension is T2 . The natural length of wire is

Question

The length of a metal wire is l1 when the tension in it is T1 and is l2 when the tension is T2 . The natural length of wire is (A) (l1 + l2/2) (B) √l1 l2 (C) (l1 T2 - l2 T1/T2 - T1) (D) (l1 T2 + l2 T1/T2 + T1)

Tardigrade Admin · Accepted Answer

Let the original length be l . In first case, l1=l+dl1 Using Hooke's law, x=(T/K) Where, x is the displacement. We have, l1=l+(T1/K) ... (i) Similarly, l2=l+(T2/K) ... (ii) Solving Equations. (i) and (ii), we get l=(l1 T2 - l2 T1/T2 - T1)

Q. The length of a metal wire is $l_{1}$ when the tension in it is $T_{1}$ and is $l_{2}$ when the tension is $T_{2}$ . The natural length of wire is

$\frac{l _{1} + l _{2}}{2}$

$l_{1} l_{2}$

$\frac{l _{1} T _{2} - l _{2} T _{1}}{T _{2} - T _{1}}$

$\frac{l _{1} T _{2} + l _{2} T _{1}}{T _{2} + T _{1}}$

Q. The length of a metal wire is l1​ when the tension in it is T1​ and is l2​ when the tension is T2​ . The natural length of wire is

2l1​+l2​​

l1​l2​​

T2​−T1​l1​T2​−l2​T1​​

T2​+T1​l1​T2​+l2​T1​​

Let the original length be l . In first case, l1​=l+dl1​ Using Hooke's law, x=KT​ Where, x is the displacement. We have, l1​=l+KT1​​ ... (i) Similarly, l2​=l+KT2​​ ... (ii) Solving Equations. (i) and (ii), we get l=T2​−T1​l1​T2​−l2​T1​​

Q. The length of a metal wire is $l_{1}$ when the tension in it is $T_{1}$ and is $l_{2}$ when the tension is $T_{2}$ . The natural length of wire is

$\frac{l _{1} + l _{2}}{2}$

$l_{1} l_{2}$

$\frac{l _{1} T _{2} - l _{2} T _{1}}{T _{2} - T _{1}}$

$\frac{l _{1} T _{2} + l _{2} T _{1}}{T _{2} + T _{1}}$