Question

if the kinetic energy of the body is increased by 25% then percentage increase in its Momentum is

Answer 1

Pls feel free to ask more doubts

Answer 2

Given that,

The kinetic energy of the body is increased by 25%.

To find,

The percentage increase in its Momentum.

Solution,

The kinetic energy in terms of momentum is given by :

$P=\sqrt{2mE}$ .....(1)

E is initial kinetic energy

P is initial momentum

If the kinetic energy of the body is increased by 25%, new kinetic energy becomes, $E'=E+\dfrac{25E}{100}=\dfrac{5E}{4}$

New momentum becomes,

$P'=\sqrt{2mE'}\\\\P'=\sqrt{2m\dfrac{5E}{4}}$ .......(2)

Dividing equation (1) and (2), so,

$\dfrac{P}{P'}=\sqrt{\dfrac{2mE}{2m\times \dfrac{5E}{4}}} \\\\\dfrac{P}{P'}=\sqrt{\dfrac{4}{5}}$

$\dfrac{P}{P'}=0.8944\\\\P'=1.118P$

The percent increase in momentum is given by :

$P\%=\dfrac{P'-P}{P}\times 100\\\\P\%=\dfrac{1.118P-P}{P}\times 100\\\\P\%=11.8\%$

So, the percentage increase in its Momentum is 11.8 %.

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