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Mechanical Properties Of Fluids

Question
CBSEENPH11020512

Coefficient of linear expansion of brass and steel rods are straight alpha subscript 1 and straight alpha subscript 2. Lengths of brass and steel rods are l1 and l2 respectively. If (I2 - I1) is maintained same at all temperatures, which one of the following relations holds good?

  • straight alpha subscript 1 straight I subscript 2 squared space equals space straight alpha subscript 2 straight I subscript 1 squared
  • straight alpha subscript 1 squared straight I subscript 2 space equals space straight alpha subscript 2 squared straight I subscript 1 space
  • straight alpha subscript 1 straight I subscript 1 space equals space straight alpha subscript 2 straight I subscript 2
  • straight alpha subscript 1 straight I subscript 2 space equals space straight alpha subscript 2 straight I subscript 1

Solution

C.

straight alpha subscript 1 straight I subscript 1 space equals space straight alpha subscript 2 straight I subscript 2

Coefficient of linear expansion of brass = straight alpha subscript 1
Coefficient of linear expansion = straight alpha subscript 2
Length of brass and steel rods are l1 and l2 respectively.
Given,
Increase in length (l2'-l1' ) is same for all temperature.
So,
l2'-l1' = l2 - l1
rightwards double arrow space straight l subscript 2 space left parenthesis 1 plus straight alpha subscript 2 increment straight t right parenthesis minus space straight l subscript 1 space left parenthesis 1 plus straight alpha subscript 1 increment straight t right parenthesis space equals space straight l subscript 2 minus straight l subscript 1
rightwards double arrow space straight l subscript 2 space straight alpha subscript 2 space equals space straight l subscript 1 straight alpha subscript 1