Question

if the k.E is increase by 800 percentage by what percentage will linear momentum of the body increase?​

Answer 1

Given :

▪ Percentage increase in KE = 800%

To FinD :

▪ Percentage increase in linear momentum of body.

SoluTioN :

↗ Relation b/w kinetic energy of moving body and linear momentum is given by

$\bigstar\:\underline{\boxed{\bf{\blue{K=\dfrac{P^2}{2m}}}}}$

Here, mass remains constant so we can say that

$\therefore\bf\:K\propto P^2$

When the kinetic energy of a body is increased by 800%, its kinetic energy will become

$\dashrightarrow\sf\:K'=K+\dfrac{800}{100}K\\ \\ \dashrightarrow\sf\:K'=\dfrac{900}{100}K\\ \\ \dashrightarrow\bf\:\red{K'=9K}$

New momentum will become,

$\Rightarrow\sf\:\dfrac{{P'}^2}{P^2}=\dfrac{K'}{K}\\ \\ \Rightarrow\sf\:\dfrac{{P'}^2}{P^2}=\dfrac{9K}{K}\\ \\ \Rightarrow\sf\:\dfrac{P'}{P}=\sqrt{9}\\ \\ \Rightarrow\bf\:\green{P'=3P}$

Percentage increase in the momentum of the body is given by

$\twoheadrightarrow\sf\:\dfrac{P'-P}{P}\times 100=\dfrac{3P-P}{P}\times 100\\ \\ \twoheadrightarrow\sf\:\%\dfrac{\Delta P}{P}=\dfrac{2P}{P}\times 100\\ \\ \twoheadrightarrow\underline{\boxed{\bf{\gray{\%\dfrac{\Delta P}{P}=200\%}}}}\:\orange{\bigstar}$

Answer 2

QUESTION: -



▪ If the K.E. is increased by 800%, By what percentage will linear momentum of the body increase?



SOLUTION: -



▪ Relation between linear momentum and kinetic energy.....



P = √(2mK)



Where,


• P = Linear momentum



• m = mass



• K = kinetic energy



➡ Let the initial kinetic energy (Ki ) be K


Then,


The initial linear momentum ( Pi ) = √(2mk)



☆ according to the question.....



Kinetic energy of the body is increased by 800%.



Then,



➡ final kinetic energy ( Kf ) = K + K*800/100



➡ Kf = K + 8 K


➡ Kf = 9k


Thus,



• The final linear momentum of the body ( Pf ) = √(2m kf)


➡ Pf = √ ( 2m 9K)


➡ Pf = 3 √(2mK)


➡ Pf = 3 Pi



Now,



Percentage increase in linear momentum of the body ........



= [ ( Pf - Pi )/ Pi ]× 100


= [ (3 Pi - Pi )/ Pi ]× 100


= ( 2 Pi/ Pi ) × 100


= 2×100


= 200%


Hence,



➡ Linear momentum of the body will increase by 200%