### JEE Main On 8 April 2017 Question 1

##### Question: A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temeprature increases by $ \Delta T. $ The net change in its length is zero. Let l be the length of the rod, A its area of cross-section, Y its Young’s modulus, and $ \alpha $ its coefficient of linear expansion. Then, F is equal to - [JEE Online 08-04-2017]

#### Options:

A) $ IAY\alpha \Delta T $

B) $ AY\alpha \Delta T $

C) $ \frac{AY}{\alpha \Delta T} $

D) $ I^{2}Y\alpha \Delta T $

## Show Answer

#### Answer:

Correct Answer: B

#### Solution:

- Net change in length = 0 Thermal Exp.
$ =I\alpha \Delta t $

$ y=\frac{F/A}{\Delta l/l} $ $ \frac{\Delta l}{l}=\frac{F}{Ay} $ $ \frac{Fl}{Ay}=l\alpha \Delta t $ $ F=AY\alpha \Delta t $