Question

An iron bar (Young's modulus = 1011 N/m²,
c = 10-/°C 1 m long and 10-3 m2 in area is
I ted from 0°C to 100°C without being allowed to
bend or expand. Find the compressive force
developed inside the bar.
(1) 10,000 N
(2) 1000 N (N)
(3) 5000 N
(4) 105 N
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Answer 1

Given that,

The Young's modulus of an iron bar is $10^{11}\ N/m^2$

$\alpha =10^{-6}\ /^{\circ} C$

Area of iron bar, $A=10^{-3}\ m^2$

It is heated from 0°C to 100°C without being allowed to  bend or expand.

To find,

The compressive force  developed inside the bar.

Solution,

The compressive force in terms of Young's modulus is given by :

$F=AY\alpha \Delta T$

Plugging all the values in it we get :

$F=10^{-3}\times 10^{11}\times 10^{-6}\times (100-0)\\\\F=10000\ N$

So, the compressive force developed inside the bar is 10,000 N.