Answer
64.8k+ views
Hint: To find the change in kinetic energy , we need to find the kinetic energy for given two situations separately. The kinetic energy of a moving object is related to its mass and velocity by the formula
${\text{K}}{\text{.E = }}\dfrac{1}{2}m{v^2}$
Complete step by step solution:
We know for kinetic energy, body must have velocity
Let initial velocity = v
$\eqalign{
& {\text{Also Kinetic energy is equal to}} \cr
& {\text{K}}{\text{.E}}{\text{. = }}\dfrac{1}{2}m{v^2} \cr
& {\text{given velocity decreased to half , so new velocity v'}} \cr
& {\text{v' = }}\dfrac{v}{2} \cr
& \Rightarrow {\text{K}}{\text{.}}{{\text{E}}_{new}} = {\text{ }}\dfrac{1}{2}m \times {\text{ (}}\dfrac{v}{2}{{\text{)}}^2} \cr
& \Rightarrow {\text{K}}{\text{.}}{{\text{E}}_{new}}{\text{ = }}\dfrac{1}{2}m\dfrac{{{v^2}}}{4} \cr
& \therefore {\text{K}}{\text{.}}{{\text{E}}_{new}}{\text{ = }}\dfrac{{m{v^2}}}{8} \cr
& {\text{Now as asked we need to find the decrease}} \cr
& \Delta {\text{K}}{\text{.E = }}\dfrac{{m{v^2}}}{2}{\text{ - }}\dfrac{{m{v^2}}}{8}{\text{ }} \cr
& \therefore \Delta {\text{K}}{\text{.E = }}\dfrac{3}{4}m{v^2} \cr
& {\text{Kinetic energy will decrease by }}\dfrac{3}{4}th{\text{ of initial kinetic energy}} \cr} $.
Additional information: Although the concept of kinetic energy dates back to the days of Aristotle, Lord Kelvin is first credited with using the term around 1849. Kinetic energy, the form of energy that is caused by the motion of an object or particle. If work, which transfers energy, is done by applying a net force on an object, the object moves and from which kinetic energy is obtained. The kinetic energy is the property of a moving object or particle also depends not only on the speed but also on the mass. The type of movement can be translation (or movement along a path from one place to another), moving around a spindle, vibration or any combination of movements.
There are two main types of kinetic energy: translational and rotational. The translational kinetic energy depends on the motion through space, and the rotational kinetic energy depends on the motion centered on the axis.
Note: The kinetic energy for any moving object can be calculated as long as the mass and speed of the objects are known. The unit used to measure kinetic energy is called Joule. If there are units of kilograms in mass and speed of meters per second, then kinetic energy consists of units of square-kilograms-kilograms per second.
${\text{K}}{\text{.E = }}\dfrac{1}{2}m{v^2}$
Complete step by step solution:
We know for kinetic energy, body must have velocity
Let initial velocity = v
$\eqalign{
& {\text{Also Kinetic energy is equal to}} \cr
& {\text{K}}{\text{.E}}{\text{. = }}\dfrac{1}{2}m{v^2} \cr
& {\text{given velocity decreased to half , so new velocity v'}} \cr
& {\text{v' = }}\dfrac{v}{2} \cr
& \Rightarrow {\text{K}}{\text{.}}{{\text{E}}_{new}} = {\text{ }}\dfrac{1}{2}m \times {\text{ (}}\dfrac{v}{2}{{\text{)}}^2} \cr
& \Rightarrow {\text{K}}{\text{.}}{{\text{E}}_{new}}{\text{ = }}\dfrac{1}{2}m\dfrac{{{v^2}}}{4} \cr
& \therefore {\text{K}}{\text{.}}{{\text{E}}_{new}}{\text{ = }}\dfrac{{m{v^2}}}{8} \cr
& {\text{Now as asked we need to find the decrease}} \cr
& \Delta {\text{K}}{\text{.E = }}\dfrac{{m{v^2}}}{2}{\text{ - }}\dfrac{{m{v^2}}}{8}{\text{ }} \cr
& \therefore \Delta {\text{K}}{\text{.E = }}\dfrac{3}{4}m{v^2} \cr
& {\text{Kinetic energy will decrease by }}\dfrac{3}{4}th{\text{ of initial kinetic energy}} \cr} $.
Additional information: Although the concept of kinetic energy dates back to the days of Aristotle, Lord Kelvin is first credited with using the term around 1849. Kinetic energy, the form of energy that is caused by the motion of an object or particle. If work, which transfers energy, is done by applying a net force on an object, the object moves and from which kinetic energy is obtained. The kinetic energy is the property of a moving object or particle also depends not only on the speed but also on the mass. The type of movement can be translation (or movement along a path from one place to another), moving around a spindle, vibration or any combination of movements.
There are two main types of kinetic energy: translational and rotational. The translational kinetic energy depends on the motion through space, and the rotational kinetic energy depends on the motion centered on the axis.
Note: The kinetic energy for any moving object can be calculated as long as the mass and speed of the objects are known. The unit used to measure kinetic energy is called Joule. If there are units of kilograms in mass and speed of meters per second, then kinetic energy consists of units of square-kilograms-kilograms per second.
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)