A rod is found to be 0.05 ~cm longer at 40^ C than it is at 10^ C . The length of the rod at 0^ C is (coefficient of linear expansion of the material of the rod .=1.5 10⁻⁵ ^ C ⁻¹ )

Step-by-step solution

aligned & L at 10^ C = L ₀(1+10 ) & L at 40^ C = L ₀(1+40 ) & L _ 40^ C =0.05+ L _ 10^ C & L ₀+ L ₀ 40=0.05+ L ₀+10 ~L ₀ & 30 I ₀ =0.05 & ~L ₀= 0.05 30 aligned The length of the rod at 0^ C = 0.05 30 1.5 10⁻⁵ =111.1 ~cm