Question:
A Soft plastic bottle, filled with water of density $1\, gm / cc$, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure The test-tube has a mass of $5\, gm$, and it is made of a thick glass of density $25 \,gm / cc$ Initially the bottle is sealed at atmospheric pressure $p _{0}=10^{5} \,Pa$ so that the volume of the trapped air is $v _{0}=33\, cc$ When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces It is found that the test tube begins to sink at pressure $p _{0}+\Delta p$ without changing its orientation At this pressure, the volume of the trapped air is $v _{0}-\Delta v$ Let $\Delta v = X \,\,cc$ and $\Delta p = Y \times 10^{3} Pa$ The value of $Y$ is _______
A Soft plastic bottle, filled with water of density $1\, gm / cc$, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure The test-tube has a mass of $5\, gm$, and it is made of a thick glass of density $25 \,gm / cc$ Initially the bottle is sealed at atmospheric pressure $p _{0}=10^{5} \,Pa$ so that the volume of the trapped air is $v _{0}=33\, cc$ When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces It is found that the test tube begins to sink at pressure $p _{0}+\Delta p$ without changing its orientation At this pressure, the volume of the trapped air is $v _{0}-\Delta v$ Let $\Delta v = X \,\,cc$ and $\Delta p = Y \times 10^{3} Pa$ The value of $Y$ is _______
Updated On: Feb 8, 2024
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Correct Answer: 10
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Answer: 10.00
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Concepts Used:
Pressure
Pressure is defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Everyday examples of pressure are:
- The working of the vacuum cleaner is an example of pressure. The fan inside the vacuum creates a low-pressure region which makes it easy to suck the dust particles inside the vacuum.
- Using a knife for cutting is another example of pressure. The area exposed from the knife is small but the pressure is high enough to cut the vegetables and fruits.
Formula:
When a force of ‘F’ Newton is applied perpendicularly to a surface area ‘A’, then the pressure exerted on the surface by the force is equal to the ratio of F to A. The formula for pressure (P) is:
P = F / A
Units of Pressure:
The SI unit of pressure is the pascal (Pa)
A pascal can be defined as a force of one newton applied over a surface area of a one-meter square.