A steel rod of cross-sectional area 4cm2 and length 2m shrinks by 0.1cm as the temperature decreases in night. If the rod is clamped at both ends during the day hours, find the tension developed in it during night hours. Young's modulus of steel = 1.9x1011N/m2.


Share with your friends
Call

Length of the rod =L =2 m 

The length increased during the night = l =0.1 cm= 0.001 m 

The strain developed during the night =l/L =0.001/2 =0.0005 

If the tension developed = T N 

The stress developed = T/A N/m² 

= T/0.0004 N/m² 

But stress = strain*Y 

T/0.0004 = 0.0005*1.9 ×10¹¹ N 

→T = 0.0004*0.0005*1.9×10¹¹ N 

→T= 2×10⁻⁷*1.9×10¹¹ N 

→T= 3.8x10⁴ N