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State and prove Pascal's law. |
Answer» Solution :Law : The pressure in a fluid at rest is the same at all points  PROOF of Pascal.s law. ABC-DEF is an element of the interior of a fluid at rest , This element is in the form of a right angled PRISM . The element is SMALL sothat the effect of gravity can be ignored, but it has been enlarged for the sake of clarity .  Figure shows an element in the interior of a fluid at rest . This element ABC- DEF is in the form of a right - angled prism. Area of surface ADFC is `A_(b)`. The force on this surface is `F_(b)` and hence pressure is `P_(b)`. Area of surface BEFC is `A_(a)` . The PERPENDICULAR force on this surface is `F_(a)` and hence pressure is `P_(a)`. Area of surface ABCD is `A_(c)` .The perpendicular force on this surface is `F_(c)` and hence pressure is `P_(c)` `F_(a)=F_(b)costheta` (For equilibrium position) `A_(a)=A_(b)costheta` (by geometry )and `F_(c)=F_(b)SINTHETA` (for equilibrium position) `A_(c)=A_(b)sintheta` (by geometry) The pressures on rectangular surfaces are as below as shown in figure. `P_(b)=(F_(b))/(A_(b))`....(1) `P_(a)=(F_(a))/(A_(a))=(F_(b)costheta)/(A_(b)costheta)=(F_(b))/(A_(b))`....(2) `P_(c)=(F_(c))/(A_(c))=(F_(b)sintheta)/(A_(b)sintheta)=(F_(b))/(A_(b))`....(3) It is clear from equation1,2 and 3 `P_(a)=P_(b)=P_(c)` .... (4) Equation (4) shows that pressure exerted is same in all directions is a fluid at rest . |
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