When a thin rod of length `'l'` is heated from `t_(1)^(0)C` to `t_(2)^(0)C` length increases by `1%` . If plate of length `2l` and breadth `'l'` made of same material is heated form `t_(1)^(0)C` to `t_(2)^(0)C`, percentage increase in area is

Options

A. `1%`
B. `3%`
C. `4%`
D. `2%`

Explanation

To solve the problem step by step, we will analyze the linear expansion of the rod and then apply the concept of superficial expansion for the plate.

### Step 1: Understand the given information
We are given that a thin rod of length \( l \) is heated from \( t_1 \) to \( t_2 \) and its length increases by \( 1\% \). This means the change in length \( \Delta L \) can be expressed as:
\[ \Delta L = \frac{1}{100} l = 0.01 l \]

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