Question

when a thin rod of length l is heated from t1c to t2c length increases by 1%. if plate of length 2 l and breadth l made of same material is heated form t1c to t2c , percentage increase in area is

Answer 1

Coefficient of area expansion is twice of linear expansion for the same material

Answer 2

Answer:

Concept :

By comparing a shape to squares of a given size, the area of a shape can be computed. The cubic kilometre (written as m2), which is the surface of a square with one-metre-long sides, is the standard unit of area in the Worldwide System of Units (SI). A three-square-metre shape has the same area as three identical squares. The area of the unit square is one, while the area about any other shape or surfaces is a non - dimensional real number in mathematics.

Given :

The length of a thin rod of length l increases by 1% when warmed from t1 to t2 degrees Celsius. When a plate with a length of 2 l and a width of l made of the same material is heated from t1 to t2 degrees Celsius, the percentage increase in area is

Find :

To find the percentage increase in area

Answer :

The percentage increase in area is 2

Explanation :

Here we know that,

$l_{2} =l_{1}$(1+alpha dt)

$dt=t_{2} -t_{1}$ degree centigrade

$\frac{l_{2}-l_{1} }{l_{1} } =alpha, dt$

percentage change in length = $=[(l_{2}-l_{1})/l_{1} ]*100 = alpha, dt100=1$

$alpha=1/(100dt)\\beta=2/(100dt)$

percentage change in area $= [(A_2-A_1)/A1]*100=beta, dt100$

                                             $=2$

Hence, The percentage increase in area is 2

divide the increase by the original number and multiply the result by 100 to find the difference between the two values being compared.

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