A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has highe

Q: Why doesn't the strip just shrink straight down?

Because the two metals are welded together! If they shrank independently, $A$ would just be shorter than $B$. But since they are attached, the only geometric way for one side to be shorter than the other is to form a curve, where the shorter side becomes the inner radius.

Q: What if we heated the strip instead of cooling it?

If heated, $\Delta T$ is positive. Metal $A$ would expand more than metal $B$. To accommodate $A$ being longer, it would form the outer radius of the curve, meaning the strip would bend towards $B$ (the right).

Q: Does the thickness of the strip matter?

Yes, the exact radius of curvature depends on the thickness of the metals and their Young's moduli. However, the *direction* of bending depends purely on the difference in their thermal expansion coefficients.

Q: What does 'mounted rigidly' mean here?

It means the base of the strip cannot move or rotate. The bending must start from the base and curve upwards, much like a tree bending in the wind.

Q: Is it possible for the strip to break instead of bending?

In extreme temperature changes, the thermal stresses can exceed the yield strength or the strength of the weld, causing it to warp permanently or break. But in standard physics problems, we assume ideal elastic bending!

Question

A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of expansion compared to that of metal B. When the bimetallic strip is placed in a cold bath, it will

Options:

(A) bend towards the right

(B) not bend but shrink

(C) Neither bend nor shrink

(D) bend towards the left

Sigma Percentile · Accepted Answer

The behavior of a bimetallic strip under temperature changes is one of the most elegant demonstrations of thermal expansion. It’s a classic physics problem that tests your intuition about how materials respond to heat and cold. Let's break down the mechanics of this bending phenomenon step by step. ### The Setup: A Tale of Two Metals Imagine you have a bimetallic strip made of two different metals, $A$ and $B$, welded tightly together along their length. They are standing straight up, perfectly happy and in equilibrium at room temperature. The problem gives us a crucial clue: the coefficient of linear thermal expansion of metal $A$ is greater than that of metal $B$ ($\alpha_A > \alpha_B$). What does this mean physically? It means metal $A$ is more sensitive to temperature changes. If you heat them, $A$ will expand more than $B$. If you cool them, $A$ will shrink more than $B$. ### The Physics of Shrinking Now, we plunge this strip into a cold bath. The temperature drops, meaning the change in temperature $\Delta T$ is negative. Let's look at the governing equation for linear thermal expansion: $$ \Delta L = L_0 \alpha \Delta T $$ Since $\Delta T < 0$, the change in length $\Delta L$ for both metals will be negative. They both want to shrink. However, because $\alpha_A > \alpha_B$, the magnitude of the contraction for metal $A$ will be strictly greater than that for metal $B$: $$ |\Delta L_A| > |\Delta L_B| $$ This implies that the new length of metal $A$ becomes strictly less than the new length of metal $B$ ($L_A < L_B$). ### The Inevitable Bend Here is the catch: the two metals are welded together! They cannot just slide past each other to accommodate their new lengths. To allow metal $A$ to be shorter and metal $B$ to be longer while remaining attached, the entire strip must undergo a geometric transformation. It must bend. Think of two runners on a curved track. The runner on the inner lane covers less distance than the runner on the outer lane. Similarly, for the bimetallic strip to have one side shorter than the other, it must curve such that the shorter side forms the inner radius. Since metal $A$ is shorter, it must become the inner curve. Therefore, the strip bends towards metal $A$, which is on the left. **Conclusion:** The bimetallic strip bends towards the left. If we had heated it instead, $A$ would expand more, becoming the outer curve, and it would bend to the right. Always remember: a bimetallic strip bends towards the metal with the lower $\alpha$ when heated, and towards the metal with the higher $\alpha$ when cooled.

Animated Solution for Physics - Properties of Solids and Liquids: A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of expansion compared to that of metal B. When the bimetallic strip is placed in a cold bath, it will

Select Answer:

Visualized Solution

$I ni t ia l S e t u p$

$α_{A} > α_{B}$

$Δ T < 0$

$Δ L = L_{0} α Δ T$

$Bending Direction$

$Conclusion$

The Sigma Insight: Thermal Expansion

The Setup

The Physics of Shrinking

The Inevitable Bend

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