A wire of initial length L and radius r is stretched by a length l. Another wire of same material but with initial length 2L and radius 2r is stretched by a length 2l. The ratio of the stored elastic energy per unit volume in the first and second wire is,

Question

A wire of initial length L and radius r is stretched by a length l. Another wire of same material but with initial length 2L and radius 2r is stretched by a length 2l. The ratio of the stored elastic energy per unit volume in the first and second wire is, (A) 1: 4 (B) 1: 2 (C) 2: 1 (D) 1: 1

Tardigrade Admin · Accepted Answer

Elastic energy per unit volume of wire. μ =(1/2) × Young's modulus ×( text Strain )2 ∴ (u1/u2)= (( text Strain 1./( text Strain )2) 2=(l2/L2) × (4 L2/4 l2)=1: 1

Q. A wire of initial length $L$ and radius $r$ is stretched by a length $l$ . Another wire of same material but with initial length $2 L$ and radius $2 r$ is stretched by a length $2 l$ . The ratio of the stored elastic energy per unit volume in the first and second wire is,

1 : 4

1 : 2

2 : 1

1 : 1

Elastic energy per unit volume of wire.
$μ = \frac{1}{2} \times$ Young's modulus $\times (Strain)^{2}$
$∴ \frac{u _{1}}{u _{2}} = {\frac{( Strain _{1}}{( Strain ) _{2}}}^{2} = \frac{l ^{2}}{L ^{2}} \times \frac{4 L ^{2}}{4 l ^{2}} = 1 : 1$

Q. A wire of initial length L and radius r is stretched by a length l. Another wire of same material but with initial length 2L and radius 2r is stretched by a length 2l. The ratio of the stored elastic energy per unit volume in the first and second wire is,