Question

Two copper rods P, Q of thickness in the ratio $2:5$ are taken. If rods P, Q of same length are supplied with $200J$ of heat energy then greater expansion is possible in:

• A. Rod P
• B. Rod Q
• C. Both have same expansions
• D. None of the rod expands

Answer 1

The correct option is C Both have same expansions

Let the length of P be $2L$ and Q be $5L$

Mass of P is $2m$ and Q be $5m$ because they both have same density.

Now when 200 J is supplies to P,

$200=m_{p}c\Delta T_P=2mc\Delta T_p$

$\Delta T_p=\frac{200}{2mc}$

Expansion in P is $\Delta L_p=L_p\alpha \Delta T_p$

$\Delta L_p=2L\alpha \frac{200}{2mc}=L\alpha \frac{200}{mc}$

Now when 200 J is supplies to Q,

$200=m_{q}c\Delta T_P=5mc\Delta T_Q$

$\Delta T_Q=\frac{200}{5mc}$

Expansion in Q is $\Delta L_Q=L_Q\alpha \Delta T_Q$

$\Delta L_Q=5L\alpha \frac{200}{5mc}=L\alpha \frac{200}{mc}$

Hence $\Delta L_p=\Delta L_Q$

Thus both rods expand with same amount.