Solveeit Logo
Login

Question

Question: The length of a rod is 20 cm and area of cross-section \(2 \mathrm {~cm} ^ { 2 }\). The Young's modu...

The length of a rod is 20 cm and area of cross-section 2 cm22 \mathrm {~cm} ^ { 2 }. The Young's modulus of the material of wire is 1.4×1011 N/m21.4 \times 10 ^ { 11 } \mathrm {~N} / \mathrm { m } ^ { 2 }. If the rod is compressed by 5 kg-wt along its length, then increase in the energy of the rod in joules will be

A

8.57×10−68.57 \times 10 ^ { - 6 }

B

22.5×10−422.5 \times 10 ^ { - 4 }

C

9.8×10−59.8 \times 10 ^ { - 5 }

D

45.0×10−545.0 \times 10 ^ { - 5 }

Answer

8.57×10−68.57 \times 10 ^ { - 6 }

Explanation

Solution

Energy = 12Fl=12×F×(FLAY)=12×F2LAY\frac { 1 } { 2 } F l = \frac { 1 } { 2 } \times F \times \left( \frac { F L } { A Y } \right) = \frac { 1 } { 2 } \times \frac { F ^ { 2 } L } { A Y }

=12×(50)2×20×10−22×10−4×1.4×1011= \frac { 1 } { 2 } \times \frac { ( 50 ) ^ { 2 } \times 20 \times 10 ^ { - 2 } } { 2 \times 10 ^ { - 4 } \times 1.4 \times 10 ^ { 11 } }