Question

The linear momentum of abody is increased by 10% what is the percentage increase in kinetic energy???

Answer 1

The momentum will increase 1.414 times or 41.4 %

We have,
Kinetic energy,

K = 1/2 mv^2
 
Where 'm' is the mass of the object and 'v' is the velocity of linear motion.
 
Similarly,
Linear momentum,

P = mv
 
On solving the 2 equations, we get the direct relation between P and K.
 
 K = P^2/2m
 
 Or k is propotional to P^2
 
It is said that linear Kinetic energy raised by 100%, so new Kinetic energy,
K*= 2 K
 
To find the new momentum P*,
 
K∗/K=(P∗/P)2K∗/K=(P∗/P)2

2K/K=(P∗/P)22K/K=(P∗/P)2

2=(P∗/P)22=(P∗/P)2

P∗=√2PP∗=√2P

The momentum increases √2 times.


Hope this helps....