Question

When kinetic energy of bodybid increased by 800% , then percentage change in its linear momentum is?

Answer 1

Kinetic energy directly proportional to square of linear momentum that swhy        linear momentum will increase by 200% /%change in linear momentum=3-1/1*100=200%

Answer 2

Given :

Kinetic energy of body bid increased by 800% .

To Find :

The percentage change in its linear momentum .

Solution :

Let , Initial mass, initial velocity and final velocity is m,u and v .

So , its kinetic energy , $K.E_i=\dfrac{mu^2}{2}$

Now , final energy is given by :

$K.E_f=\dfrac{mv^2}{2}$

$K.E_f=K.E_i+800 \% \ of\ K.E_i\\\\K.E_f=\dfrac{mu^2}{2}+\dfrac{800}{100} \times \dfrac{mu^2}{2}\\\\K.E_f=\dfrac{9mu^2}{2}$

Therefore ,

$\dfrac{mv^2}{2}=\dfrac{9mu^2}{2}\\\\v = 3u$

Now , change in momentum

$=\dfrac{P_f-P_i}{P_i} \times 100 \\\\=\dfrac{mv-mu}{mu} \times 100 \\\\=\dfrac{3u-u}{u}\times 100\\\\=200\ \%$

Therefore , percentage change in its linear momentum is 200 % .

Hence , this is the required solution .