A) \[gd\left( \frac{{{H}_{1}}-{{H}_{2}}}{2} \right)\]
B) \[{{g}^{2}}{{d}^{2}}{{a}^{2}}{{\left( \frac{{{H}_{1}}-{{H}_{2}}}{2} \right)}^{2}}\]
C) \[adg{{\left( \frac{{{H}_{1}}-{{H}_{2}}}{2} \right)}^{2}}\]
D) \[\frac{{{({{H}_{1}}-{{H}_{2}})}^{2}}}{2ga}\]
Correct Answer: C
Solution :
Consider the diagram As volume of water is constant, so finally, height water level in each vessel will be \[\frac{{{H}_{1}}+{{H}_{2}}}{2}.\] The mass per unit volume of water \[m=d\,a\,\left[ {{H}_{1}}-\frac{{{H}_{1}}+{{H}_{2}}}{2} \right]\] \[=ad\left[ \frac{{{H}_{1}}-{{H}_{2}}}{2} \right]\] Now, work done by gravity \[=mg\cdot x=ad\left( \frac{{{H}_{1}}-{{H}_{2}}}{2} \right)\cdot g\cdot \left( \frac{{{H}_{1}}-{{H}_{2}}}{2} \right)\] \[\left( \because \,x=\frac{{{H}_{1}}-{{H}_{2}}}{2} \right)\] \[\Rightarrow \] \[{{W}_{mg}}=adg{{\left( \frac{{{H}_{1}}-{{H}_{2}}}{2} \right)}^{2}}\]You need to login to perform this action.
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