A) \[\frac{mgh}{4}\]
B) \[\frac{mgh}{2}\]
C) \[mgh\]
D) \[2mgh\]
Correct Answer: B
Solution :
The mass of the liquid in a column between \[x\]and \[x+dx\]is \[dm=\pi {{r}^{2}}\rho dx.\]Therefore, the potential energy of the liquid in a column of height h is \[\int_{0}^{b}{(\pi {{r}^{2}})}x\,\rho gdx\] \[=\pi {{r}^{2}}\rho g\int_{0}^{b}{xdx}\] \[=\pi {{r}^{2}}\rho g\frac{{{h}^{2}}}{2}=(\pi {{r}^{2}}h\rho )gh/2=mgh/2\] Hence the correct choice is (b).
You need to login to perform this action.
You will be redirected in
3 sec
