Answer
417k+ views
Hint:First of all, we will find the weight force of the automobile, which is simply the function of mass and acceleration due to gravity. Then we will find the pressure, which is termed as force per unit area. We will substitute the required values and obtain the answer.
Complete step by step solution:
In the given question, we are supplied the following data:
There is a hydraulic automobile lift which is designed to lift cars. The maximum capacity that the lift can hold with getting collapsed is \[3000\,{\text{kg}}\]. The area of the cross section of the piston that is carrying the load is \[425\,{\text{c}}{{\text{m}}^2}\]. We are asked to find the maximum pressure that the smaller have to bear.
To begin with, as we can see that the maximum capacity of the lift is given, in terms of mass. We can proceed to solve the numerical after we get the weight of the car with maximum mass. Let us proceed to solve the numerical. We know, weight force which is a function of mass and acceleration due to gravity, is given by the formula, which is shown below:
\[F = m \times g\] …… (1)
Where,
\[F\] indicates the weight force.
\[m\] indicates the mass of the car.
\[g\] indicates acceleration due to gravity.
Now, we substitute the required values in the equation (1) and we get:
$F = m \times g \\
\Rightarrow F = 3000 \times 9.8 \\
\Rightarrow F = 29400\,{\text{N}} \\$
Therefore, weight force is found to be \[29400\,{\text{N}}\] .
Again, we know the pressure is related to the force by a relation, as given below:
\[P = \dfrac{F}{A}\] …… (2)
Where,
\[P\] indicates the pressure.
\[A\] indicates the area of the cross section of the piston.
Now, we substitute the required values in the equation (2), we get:
$\Rightarrow P = \dfrac{{29400\,{\text{N}}}}{{425\,{\text{c}}{{\text{m}}^2}}} \\
\Rightarrow P = \dfrac{{29400\,{\text{N}}}}{{425 \times {{\left( {{{10}^{ - 2}}} \right)}^2}\,{{\text{m}}^2}}} \\
\Rightarrow P = \dfrac{{29400\,{\text{N}}}}{{425 \times {{10}^{ - 4}}\,{{\text{m}}^2}}} \\
\therefore P = 6.92 \times {10^6}\,{\text{Pa}} \\$
Hence, the maximum pressure that the smaller have to bear is \[6.92 \times {10^6}\,{\text{Pa}}\].
Note:While solving this problem, most of the students forget to convert the unit of the area of the cross section, which is square centimetres to square metres. Students get wrong and irrelevant answers, due to this reason. It is important to remember that smaller is the cross-sectional area of the object, higher is the pressure. Due to this reason a needle can easily go inside another object due to its small cross-sectional area.
Complete step by step solution:
In the given question, we are supplied the following data:
There is a hydraulic automobile lift which is designed to lift cars. The maximum capacity that the lift can hold with getting collapsed is \[3000\,{\text{kg}}\]. The area of the cross section of the piston that is carrying the load is \[425\,{\text{c}}{{\text{m}}^2}\]. We are asked to find the maximum pressure that the smaller have to bear.
To begin with, as we can see that the maximum capacity of the lift is given, in terms of mass. We can proceed to solve the numerical after we get the weight of the car with maximum mass. Let us proceed to solve the numerical. We know, weight force which is a function of mass and acceleration due to gravity, is given by the formula, which is shown below:
\[F = m \times g\] …… (1)
Where,
\[F\] indicates the weight force.
\[m\] indicates the mass of the car.
\[g\] indicates acceleration due to gravity.
Now, we substitute the required values in the equation (1) and we get:
$F = m \times g \\
\Rightarrow F = 3000 \times 9.8 \\
\Rightarrow F = 29400\,{\text{N}} \\$
Therefore, weight force is found to be \[29400\,{\text{N}}\] .
Again, we know the pressure is related to the force by a relation, as given below:
\[P = \dfrac{F}{A}\] …… (2)
Where,
\[P\] indicates the pressure.
\[A\] indicates the area of the cross section of the piston.
Now, we substitute the required values in the equation (2), we get:
$\Rightarrow P = \dfrac{{29400\,{\text{N}}}}{{425\,{\text{c}}{{\text{m}}^2}}} \\
\Rightarrow P = \dfrac{{29400\,{\text{N}}}}{{425 \times {{\left( {{{10}^{ - 2}}} \right)}^2}\,{{\text{m}}^2}}} \\
\Rightarrow P = \dfrac{{29400\,{\text{N}}}}{{425 \times {{10}^{ - 4}}\,{{\text{m}}^2}}} \\
\therefore P = 6.92 \times {10^6}\,{\text{Pa}} \\$
Hence, the maximum pressure that the smaller have to bear is \[6.92 \times {10^6}\,{\text{Pa}}\].
Note:While solving this problem, most of the students forget to convert the unit of the area of the cross section, which is square centimetres to square metres. Students get wrong and irrelevant answers, due to this reason. It is important to remember that smaller is the cross-sectional area of the object, higher is the pressure. Due to this reason a needle can easily go inside another object due to its small cross-sectional area.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)