NAEST 2020: Pressure and Force on a Lota and Measuring Cylin
By Question: 1: In the later part of the video, the Lota and the measuring cylinder both are filled with water and kept side by side. Take the pressure due to water on the base of the Lota (Vessel) to be $P_1$ and that on the base of the Measuring Cylinder to be $P_2$. Atmospheric pressure is $P_0$. Choose the correct option.
- $P_1 = P_2$
- $P_1 > P_2$
- $P_1 < P_2$
- $P_1 = P_2 = P_0$
- $F_1 = F_2$
- $F_1 > F_2$
- $F_1 < F_2$
- $F_1$ and $F_2$ depend on the area of the base of the containers
Solution 1: The pressure at the top of container (cylinder as well as lota) is equal to the atmospheric pressure $P_0$. The pressure at the base of the container is equal to $P_0$ plus the hydrostatic pressure due to water column. The height of water column for lota is $h_1$ and that for the cylinder is $h_2\, ( > h_1)$. Thus, pressures due to water at the base of the lota and the cylinders are
\begin{align}
P_1 & = P_0+\rho g h_1, \\
P_2 & = P_0+\rho g h_2,
\end{align}
where $\rho$ is the density of water and $g$ is acceleration due to gravity. Since $h_1 < h_2$, we get $P_1 < P_2$.
The pressure at the base depends on the height of the water column. It is independent of the shape of the container.
Solution 2: The volume (and hence mass) of water is same in both the containers. The forces acting on the water are (i) its downward weight $mg$, (ii) downward force at top due to air pressure, and (iii) the force by the container. Let area of the lota exposed to the air be $A_1$ and that of the cylinder be $A_2\, ( < A_1) $. Since water is at rest, resultant force on the water is zero, which gives
\begin{align}
mg + P_0 A_1 = F_{1c}, \\
mg + P_0 A_2 = F_{2c}.
\end{align}
Since $A_1 > A_2$, we get $F_{1c} > F_{2c}$. By Newton's third law, the force applied by the container on the water is equal and opposite to the force applied by the water on the container i.e., $F_1 = F_{1c} $ and $F_2 = F_{2c} $. Hence, we get $F_1 > F_2$. The force applied by the water on the lota is greater than the force applied by the water on the cylinder.
If you measure the weight of the water-filled lota and the water-filled cylinder using a pan balance then you will get the same or different values? Why the effect of air pressure is neglected in measurements done at grocery shop?
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