A) \[\frac{ad}{g}\]
B) \[\frac{ag}{d}\]
C) \[\frac{a}{d}\]
D) \[\frac{dg}{a}\]
Correct Answer: A
Solution :
[a] Mass of liquid in horizontal portion of U-tube\[=Ad\rho \] Pseudo force on this mass\[=Ad\rho a\] Force due to pressure difference in the two limbs \[=({{h}_{1}}\rho g-{{h}_{2}}\rho g)A\] Equating both the forces \[({{h}_{1}}-{{h}_{2}})\rho gA=Ad\rho a\] \[\Rightarrow \,\,({{h}_{1}}-{{h}_{2}})=\frac{Ad\rho a}{\rho gA}=\frac{ad}{g}\]
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