Question

There are two round tables in the physics classroom: one with a radius of 50 cm, the other with a radius of 150 cm. What is the relationship between the two forces applied to the tabletops by the atmospheric pressure? then the value of $\dfrac{{{F_1}}}{{{F_2}}}$ is:
A) $\dfrac{1}{9}$
B) $\dfrac{1}{3}$
C) $3$
D) $\text{None of these}$

Answer 1

Hint: The force is defined as a push or pull of an object that causes a change in the state of rest or motion thereby causing a change in the direction or the shape of an object. The force causes the object to accelerate. The pressure is defined as the force applied perpendicular to the surface per unit area.

Complete step by step solution:
Given data:
The radius of the first table, ${r_1} = 50cm$
The radius of the second table, ${r_2} = 150cm$
Let the pressure in both the tables $ = P$ ($\because $ the atmospheric pressure is the same for both the tables)
Let the force of the first table $ = {F_1}$
Let the force of the second table $ = {F_2}$
We know the formula, $Pressure = \dfrac{{Force}}{{Area}}$
 Area of the first table, \[{A_1} = \pi \times {\left( {50} \right)^2}\]
Area of the second table, \[{A_2} = \pi \times {\left( {150} \right)^2}\]
Thus ${F_1} = P{A_1} = P \times \pi \times {\left( {50} \right)^2}\_\_\_\_\_\_\_\_\left( 1 \right)$ and
${F_2} = P{A_2} = P \times \pi \times {\left( {150} \right)^2}\_\_\_\_\_\_\_\left( 2 \right)$
Dividing the two equations, we get $\dfrac{{{F_1}}}{{{F_2}}} = \dfrac{{P \times \pi \times {{\left( {50} \right)}^2}}}{{P \times \pi \times {{\left( {150} \right)}^2}}} = \dfrac{{2500}}{{22500}} = \dfrac{1}{9}$

Hence the correct option is A.

Note: 1. The pressure that is exerted by the atmosphere on the earth is called Atmospheric Pressure. It is measured by using a barometer. It depends on the weather conditions, it changes when the temperature changes. As the height increases, atmospheric pressure decreases which is due to the increase in the altitude.
2. Also the air pressure is an indication of the weather. Usually wind, cloudiness indicates that a low-pressure system is moving. Calm weather indicates that a high-pressure system is leading. The main factors that affect air pressure are altitude, temperature, moisture.
3. In general we do not feel the atmospheric pressure on us. The reason is that the air which is present in our bodies will exert the same pressure outwards and hence there is no need to exert any effort.