Question

A rod of length l and area of cross-section A, is heated from $0^{\circ }C$ to ${100}^{\circ }C$. The rod is so placed that it is not allowed to increase in length, then the force developed is proportional to ?

• A. $l$
• B. $l^{-3}$
• C. $A$
• D. $A^{-1}$

Answer 1

The correct option is C $A$

Lets consider, $l=$ length of the rod

$A=$ cross-sectional area

In linear thermal expansion,

strain, $\frac{\Delta l}{l}=\alpha \Delta T$. . . . . . . . .(1)

Thermal Stress, ${\sigma }_{th}=Y\times strain=Y\alpha \Delta T$. . . . . . .(2)

where, $Y=$ young's modulus of the material

We know that, Stress, $\sigma =\frac{F}{A}$. . . . . .(3)

From equation (2) and equation (3) we get,

$\frac{F}{A}=Y\alpha \Delta T$

$F=Y\alpha \Delta T.A$

$Y$ and $\alpha$ are the property of the material and the $\Delta T={100}^{0}C$

$F\propto A$

Force developed is directly proportional to Area $A.$

The correct option is C.