A metal rod has length of 100 cm and cross-section of `1.0 cm^(2)`. By raising its temperture from `0^(@)C` to `100^(@)C` and holding it so that it is not permitted to expand or bend, the force developed is (Given `Y=10^(12)` dyne `cm^(-2)` and `alpha=10^(-5) .^(@)C^(-1)`)

Options

A. `10^(8)` dyne
B. `10^(9)` dyne
C. `10^(10)` dyne
D. `10^(14)` dyne

Answer

B

Explanation

From, `Y=(F l)/(A Delta l), Delta l(F l)/(AY)`
Increase in length on heating, `Delta l=alpha l Delta T` When the bar is permitted neither to expand nor to bend, then `Delta l=(F l)/(AY)=alpha l Delta T`
or `F=A Y alpha Delta T`
`=1xx10^(12)xx10^(-5)xx100 =10^(9)` dyne