Question

If the kinetic energy if a body is increased to x times, its momentum increases to _______ times.

(a)x^3
(b)√x
(c)x^2
(d)x^4

Answer 1

Answer

• ( b ) √x

$\orange{\bigstar}$  Given  $\green{\bigstar}$

The kinetic energy if a body is increased to x times

$\orange{\bigstar}$  To Find  $\green{\bigstar}$

It's momentum increases to how many times

$\orange{\bigstar}$  Key points  $\green{\bigstar}$

$\bullet \;\; \bf K.E=\dfrac{P^2}{2m}\\\\\to \bf P^2=2m(K.E)$

$\orange{\bigstar}$  Solution  $\green{\bigstar}$

Let ,

K = Kinetic energy

m = mass of an object

P = momentum

So  Momentum is ,

$\to \rm P^2=2mK\\\\\to \rm P=\sqrt{2mK}\\\\\to \bf P\ \propto \sqrt{K}\ ...(1)$

Now , when Kinetic energy , K is increased to x times ,

⇒ K' = xK

So , New momentum will be ,

$\rm \to P'\ \propto \sqrt{K'}\\\\\rm \to P'\ \propto \sqrt{xK}\\\\\rm \to P'\ \propto \sqrt{x}(\sqrt{K})\\\\\bf \to P'\ \propto \sqrt{x}(P)$

So , New momentum will be increased to √x times the old momentum

Answer 2

GiveN :

• Kinetic Energy of body is increased by x times.

To FinD :

• Increase in momentum

SolutioN :

We've a relation :

⇒K.E = p²/2m

⇒ p² = 2*K.E*m

⇒ p = √(2 * K.E *m)

Where , m and 2 are constant

⇒ p ∝ √K.E ....(1)

_____________________

⇒K.E' = x * K.E

If Kinetic Energy is increased by x times then momentum is :

⇒p' ∝ √K.E'

⇒p' ∝ √(x * K.E)

⇒p' ∝ √x * √K.E

⇒p' ∝ √x * p_______(From 1)

⇒p' ∝ √x * p

✪ Hope it Helps

ㅤㅤㅤㅤㅤㅤㅤㅤ-TheDarkSlayer