Question

If the kinetic energy of a body is quadrupled,what is the change in its momentum?solve through process.​

Answer 1

QUESTION -

If the kinetic energy of a body is

quadrupled,what is the change in its momentum?

ANSWER -

Let,

Initial Momentum = Pi = mivi and,

Initilal Kinetic Energy = KE i = 1/2 mivi2

Now, it is given that the momentum is doubled.

Thus, New Momentum = Pf = mfvf = 2Pi = 2mivi

From here, vf = 2mivi/mf

And, New Kinetic Energy = KEf = 1/2 mfvf2 = 1/2 mf x (2mivi/mf)2 = 1/2 x 4 x mf/mf2 x mi2vi2

= 2 x m2/m2 x mvi2 = 2mvi2 = 4 x KEi

Note that mi = mf = m as mass doesn 't change in this case.

Thus, the kinetic energy becomes 4 times the initial.

@HARSHpratapSingh

Answer 2

Answer:

KE = (P²)/(2m)

KE = Kinetic energy

P = Momentium

m = mass

If the momentum of the object is doubled then

KE is directly propotional to Square of the momentium

So...

(KE1)/(P²1) = (KE2)/(P²2)

KE1 = E

KE2 = x(?)

P²1 = P

P²2 = 4P

Therefore

E/P = x/4P

x = 4E

Thus KE increases by 4 times when momentum is doubled.

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