Question

If the kinetic energy of an object is increased by 50% find the increase in the momentum of the body

Answer 1

Given :-

Kinetic Energy (K) is increased by 50 %

To Find :-

Increase in momentum (P) = ?

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Their are two methods :-

Method No. 1 :-

$\large{\boxed{\sf K={\frac{{P}^{2}}{2m}}}}$

K = 1 + 0.5K

K = 1.5K

$\large{\sf P=\sqrt{1.5}P}$

We know that value of $\sf{\sqrt{1.5}=1.224}$

So,

$\large\implies{\sf 1.224}$

$\large\implies{\sf 1+0.224}$

$\large\implies{\sf 22.4}$%

Hence ,

$\large\red{\boxed{\sf Increase\:in\:Momentum(P)=22.4}}$%

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Method No. 2 :-

Kinetic Energy (K) = increase by 50%

$\large{\sf P={\frac{\sqrt{2m(1.5K)}-\sqrt{2mK}}{\sqrt{2mK}}}}$

$\large\implies{\sf =\sqrt{1.5}-1}$

$\large\implies{\sf 1.224-1}$

$\large\implies{\sf 0.224}$

$\large\implies{\sf 22.4}$%

Hence,

$\large\red{\boxed{\sf Momentum\:Increased\:by(P)=22.4}}$%

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