Answer
64.8k+ views
Hint As we have to find the work done by the gravitational force, To calculate the work done by the gravitational force, we will adopt a simplifying approach and will assume that air resistance is negligible.
Complete step by step solution
Correct answer is $5000J$
As given
The height of the cubical vessel:
$h = 1m$
Here $h$ is the height of the vessel (total height)
Center of mass (COM) of the vessel is located at $\dfrac{h}{2}$
So, we can write
$h' = \dfrac{h}{2} = \dfrac{1}{2}m$
Also, the volume of the vessel (water) would be
${h^3} = {1^3} = 1{m^3}$
And mass of the water would be
$m = \rho V$
So we get
$m = 1000 \times 1 = 1000kg$
Because density of the water is $1000kg/{m^3}$
Now as we have to find the work done by the gravitational force
So work done for pumping out water is equal to the negative of change in its potential energy.
Hence,
$W = - \Delta P.E$
Where W is the work done which is equal to change in potential energy
Therefore,
$W = - (P.{E_f} - P.{E_i})$
$P.{E_f}$ is the final potential energy and
$P.{E_i}$ is the initial potential energy
After taking water out the final potential energy $P.{E_f}$ would be 0
And initial potential energy $P.{E_i}$ would be the initial potential energy which would be equal to $mgh'$
So, we get
$W = - (0 - mgh')$
$W = mgh'$
On putting values we get
$W = 1000 \times 10 \times \dfrac{1}{2} = 5000J$
Note Remember while measuring the energy the height should always be measured from the center of mass (COM) and moreover always use units carefully as in this case the value of the density of water must be put carefully.
Complete step by step solution
Correct answer is $5000J$
As given
The height of the cubical vessel:
$h = 1m$
Here $h$ is the height of the vessel (total height)
Center of mass (COM) of the vessel is located at $\dfrac{h}{2}$
So, we can write
$h' = \dfrac{h}{2} = \dfrac{1}{2}m$
Also, the volume of the vessel (water) would be
${h^3} = {1^3} = 1{m^3}$
And mass of the water would be
$m = \rho V$
So we get
$m = 1000 \times 1 = 1000kg$
Because density of the water is $1000kg/{m^3}$
Now as we have to find the work done by the gravitational force
So work done for pumping out water is equal to the negative of change in its potential energy.
Hence,
$W = - \Delta P.E$
Where W is the work done which is equal to change in potential energy
Therefore,
$W = - (P.{E_f} - P.{E_i})$
$P.{E_f}$ is the final potential energy and
$P.{E_i}$ is the initial potential energy
After taking water out the final potential energy $P.{E_f}$ would be 0
And initial potential energy $P.{E_i}$ would be the initial potential energy which would be equal to $mgh'$
So, we get
$W = - (0 - mgh')$
$W = mgh'$
On putting values we get
$W = 1000 \times 10 \times \dfrac{1}{2} = 5000J$
Note Remember while measuring the energy the height should always be measured from the center of mass (COM) and moreover always use units carefully as in this case the value of the density of water must be put carefully.
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the common property of the oxides CONO and class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The area of square inscribed in a circle of diameter class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Other Pages
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In the ground state an element has 13 electrons in class 11 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Electric field due to uniformly charged sphere class 12 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
According to classical free electron theory A There class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)