Question

(A): Two rods of the same material have the same lengths but diameters are in the ration of 1:2. If 1000 cal of heat is supplied to the two rods separately the ratio of their linear expansion is 8:1.
(B): The linear expansion $e=l\alpha \Delta t$

• A. A and B are correct and B is correct
  explanation for A
• B. A and B are correct and B is not correct
  explanation for A
• C. A is true and B is false
• D. A is wrong and B is true.

Answer 1

The correct option is D A is wrong and B is true.

Since the material is same, both have same density, coefficient of linear expansion and specific heat.

Area of second rod is four times that of the first rod.

Since equal amount of heat is given to different amount of masses, the change in temperature would be different.

$m_{1}C\Delta T_1=m_{2}C\Delta T_2$

$\rho \left(LA\right)C\Delta T_1=\rho \left(4LA\right)C\Delta T_2$

$⟹\Delta T_2=\frac{\Delta T_1}{4}$

Elongation =$L_0\alpha \Delta T\propto \Delta T$

Hence, ratio of elongation is 4:1.