Question

The coefficient of linear expansion of brass and steel are α₁ and α₂. If we take a brass rod of length L₁ and steel rod of length L₂ at $\left( L _ { 2 } - L _ { 1 } \right)$ will remain the same at any temperature if

• A. $\alpha _ { 1 } L _ { 2 } = \alpha _ { 2 } L _ { 1 }$
• B. $\alpha _ { 1 } L _ { 2 } ^ { 2 } = \alpha _ { 2 } L _ { 1 } ^ { 2 }$
• C. $\alpha _ { 1 } ^ { 2 } L _ { 1 } = \alpha _ { 2 } ^ { 2 } L _ { 2 }$
• D. $\alpha _ { 1 } L _ { 1 } = \alpha _ { 2 } L _ { 2 }$

Answer 1

Answer: (B)

$\alpha _ { 1 } L _ { 2 } ^ { 2 } = \alpha _ { 2 } L _ { 1 } ^ { 2 }$

Answer 2

Difference in lengths of rods will remain same if expansion is same in both the rods.

If expansion in first rod is $l _ { 2 } = L _ { 2 } \alpha _ { 2 } \Delta \theta$

then $L _ { 1 } \alpha _ { 1 } \Delta \theta = L _ { 2 } \alpha _ { 2 } \Delta \theta$ $\therefore L _ { 1 } \alpha _ { 1 } = L _ { 2 } \alpha _ { 2 }$