An iron bar of length I and having a cross-section area A is heated from `0^(@)` to `100^(@)C`. If this bar is so held that it is not permitted to expand or bend, the force that is developed, is

Options

A. inversely proportional to the cross-sectional area of the bar
B. independent of the length of the bar
C. inversely porportional to the length of the bar
D. directly proportional to the length of the bar

Answer

b

Explanation

`Y = (FL)/(AI)`
Where, Y is young's modulus and A is area
`F = (YAI)/(L)`
From the formula for linear expansion,
`alpha = (I)/(L xx 100)`
According the condition that bar will not bend or expand.
Now, fromm Eqs. (i) and (ii) we get
`F = YA = 100 alpha`
Hence, force is independent of length L