The coefficient of linear expansion of steel and brass are and W respectively. If their difference in lengths at all temperature has to kept constant at , their lengths at should be

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answer is A.

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Detailed Solution

Concept- Steel and brass rods will expand as the temperature rises. So, using the linear expansion coefficient equation, we can calculate the new lengths of the rods. We can find the ratio of new lengths of each rod because we are dealing with the same conditions.

written as

. We can assume the length of the steel rod is

and the length of brass rod is

. Here the difference in their length kept constant as

at all temperatures. So we can write this as,

If we are increasing temperature, suppose the lengths of the rods may vary. The following equation can be used to calculate this.

, where

is the new length of the steel rod,

is the initial length of the steel rod,

is the coefficient of linear expansion of steel rod and

is the temperature change.

, where

is the new length of the brass rod,

is the initial length of the brass rod,

is the coefficient of linear expansion of brass rod and

is the temperature change.
According to the question, even if they change the initial lengths of the rods, the difference in lengths will be the same. As a result, we can write,

We can simplify this equation as,

At any temperature, the difference in lengths of steel and brass rod will be the same.

As a result, the remaining terms in the above equation will be zero. As a result, we can equate that term to zero.

The temperature change is the same for both rods in this case. So, we can take it outdoors and zero out the remaining terms.

We may deduce the length ratio of steel and brass rod from this.

The coefficients of linear expansion of steel and brass rod can be assigned in their respective locations.

We must divide all of the possibilities previously provided in the question. So we can determine which choice will follow this ratio.
Option (1) is the right answer.

, all other options are in a different ratio.
Hence, option 1 is the correct answer.

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