The temperature of a wire of length 1 metre and area of cross-section \[1\,c{{m}^{2}}\] is increased from 0°C to 100°C. If the rod is not allowed to increase in length, the force required will be \[(\alpha ={{10}^{-5}}/{}^\circ C\] and \[Y={{10}^{11}}\,N/{{m}^{2}})\] [NCERT 1976; CPMT 1982, 91]

• A. \[{{10}^{3}}N\]
• B. \[{{10}^{4}}N\]
• C. \[{{10}^{5}}N\]
• D. \[{{10}^{9}}N\]