Question

The length of a wire is 1.0 m and the area of cross-section is $1.0 \times 10 ^ { - 2 } \mathrm {~cm} ^ { 2 }$. If the work done for increase in length by 0.2 cm is 0.4 joule, then Young's modulus of the material of the wire is

• A. $2.0 \times 10 ^ { 10 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
• B. $4 \times 10 ^ { 10 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
• C. $2.0 \times 10 ^ { 11 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
• D. $2 \times 10 ^ { 10 } \mathrm {~N} / \mathrm { m } ^ { 2 }$

Answer 1

Answer: (C)

$2.0 \times 10 ^ { 11 } \mathrm {~N} / \mathrm { m } ^ { 2 }$

Answer 2

$W = \frac { 1 } { 2 } \frac { Y A l ^ { 2 } } { L }$⇒$0.4 = \frac { 1 } { 2 } \times \frac { Y \times 1 ^ { - 6 } \times \left( 0.2 \times 10 ^ { - 2 } \right) ^ { 2 } } { 1 }$

∴ Y$= 2 \times 10 ^ { 11 } \mathrm {~N} / \mathrm { m } ^ { 2 }$