Question

8.
A cylindrical metal rod of length L. Young's
modulus of elasticity Y and thermal coefficient of
linear expansion a is fixed between two concrete
walls. The cross-sectional area of the rod is A. If
the temperature of the rod is increased by 10, then
the compressive force developed in the rod can be
written as
YAuΔΘ
(1)
Traso
(2) YA(ano)?
YA2010
YACAO
(3)
1-20
(4) 1- 2010​

Answer 1

Force produce in rod is 10×Y×α×A (N) and its nature is compressive.

Explanation:

1.  On increase in temperature change in length (ΔL) of rod = $L\times \alpha \times \bigtriangleup \theta$

Where L is initial length of rod; α is thermal coefficient of rod's material ; $\Delta \theta$ is increase in temperature.

2.  Strain(∈) produce in rod$\varepsilon = \frac{\Delta L}{L}$

but here length of rod decrease ,so value of change in length is in      negative.

3. So  $\varepsilon = -\alpha \times \Delta \theta$

4. Due to resistance produce by wall, Compressives tress($\sigma$) produce in rod

Stress$\sigma$ = Strain(∈)×Young's modulus of elasticity (Y)

So   $\sigma= -\alpha \times \Delta \theta \times Y$

5.  Force produce in rod (F) = Stress × Cross sectional area

So $F = -\alpha \times \Delta \theta \times Y\times A$

Negative sign meaning that nature of force produce in rod is compressive.

6.$F_{C} =\alpha \times 10 \times Y\times A= 10\alpha YA$

On putting value of increase in temperature