Question

yCiCases
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
ΥΑαΔΘ
(1) 1+ ano
(2) YA(AAO)
YA2010
YACAO
(3)
1-
10
(4) 1-2010​

Answer 1

Compressive force $(F_{c})$ developed in the rod is 10YαA (N)

Explanation:

Given

length of rod is L.

Young's modulus of elasticity is Y.

Thermal coefficient of linear expansion is α.

Cross sectional area of rod is A.

Increased in temperature($\Delta T$) is 10°C.

1.  Change in length (ΔL) of rod

    $\Delta L = L\times \alpha \times \Delta T$    

2.  Strain(∈) produce in rod =$\frac{change in length}{initial length}$

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

3. So

  $\varepsilon = \frac{-\Delta L}{L} = \frac{-L\alpha \Delta T}{L}= -\alpha \Delta T$

4. Stress($\sigma$)  produce in rod

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

   So $\sigma = - Y\alpha \Delta T$

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

    $F = - Y\alpha \Delta T\times A$

  Here negative sing indicate that force produce in rod is compressive force

6.  $F_{c} = Y\alpha \Delta T A$

 Putting value of increase in temperature

  $F_{c} = 10Y\alpha A$