A) \[F/(3\pi {{r}^{2}}YT)\]
B) \[3F/(\pi {{r}^{2}}YT)\]
C) \[6F/(\pi {{r}^{2}}YT)\]
D) \[9F/(\pi {{r}^{2}}YT)\]
Correct Answer: B
Solution :
\[\therefore \] Length of cylinder remains unchanged so\[{{\left( \frac{F}{A} \right)}_{Compressive}}={{\left( \frac{F}{A} \right)}_{Thermal}}\] \[\frac{F}{\pi {{r}^{2}}}=Y\alpha T\] (\[\alpha \]is linear coefficient of expansion) \[\therefore \]\[\alpha =\frac{F}{YT\pi {{r}^{2}}}\] \[\therefore \]The coefficient of volume expansion\[\gamma =3\alpha \] \[\therefore \]\[\gamma =3\frac{F}{YT\pi {{r}^{2}}}\]You need to login to perform this action.
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