Question

Two copper rods P and Q of thickness in the ratio $2:5$ are taken. If both the rods P and Q of length $10cm$ are heated to same temperature rise, then the ratio of the linear expansions of P to that of rod Q is :

• A. $2:5$
• B. $5:2$
• C. $1:1$
• D. $4:1$

Answer 1

The correct option is C $1:1$

Linear expansion is proportional to only length.

For P, $\Delta L_P=L_p\alpha \Delta T$

for Q $\Delta L_Q=L_Q\alpha \Delta T$

$\alpha$ is same for both the rods and $L_P=L_Q=10$

So $\frac{\Delta L_P}{\Delta L_Q}=\frac{L_P\alpha \Delta T}{L_Q\alpha \Delta T}=\frac{10}{10}=1$