A) \[\frac{DB}{B+(n-1)p}\]
B) \[\frac{DB}{B-(n-1)p}\]
C) \[\frac{DB}{B+(n\,+1)p}\]
D) None of these
Correct Answer: A
Solution :
Pressure at surface of lake = p (atoms pressure) Pressure at the depth = np (given) \[\therefore \,\, increase or cahnge in pressure \left( \Delta p \right) =np - p\] Suppose V is the volume of a certain mass M of water at the surface then \[\operatorname{M} = DV\] Now decrease in volume due to increase in pressure \[\Delta p\] is \[\Delta \,V=\frac{V\Delta p}{B}\] Volume of the mass M of water at given depth is \[V'\,\,=\,\,V-\Delta V=V\,\,-\frac{V\Delta p}{B}\] \[=\,\,\,V\left( 1-\frac{\Delta p}{B} \right)=\frac{V}{B}(B\,\,-\Delta p)\] Density of water at that depth is \[D'=\frac{M}{V'}=\frac{DV}{V'}=\frac{DV}{\frac{V}{B}(B-\Delta p)}=\frac{DB}{B-\Delta p}=\frac{DB}{B-(n-1)p}\]
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