Question

if the linear momentum is increased by 50% the kinetic energy will be increased by

Answer 1

Given :-

New Momentum = P' = 50%P + P

New momentum = P' = 50/100P + P

New momentum = P' = 0.5 P + P

New momentum =P' = 1.5P

We know that relation between kinetic energy and momentum is :-

K.E = P^2/2m --------------------(1)

Now

New kinetic energy is :-
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K.E'= P'^2 /2m

K.E'= (1.5P)^2 / 2m ----------------------(2)

Divide equation 2 by equation 1

K.E'/K.E = (1.5P)^2 /2m / P^2 /2m

Or write it as :-

K.E'/K.E = (1.5P)^2 /2m × 2m/P^2

Here 2m will cancel 2m and P will cancel P

So

K.E'/K.E = 1.5^2

K.E'/K.E = 2.25

K.E' = 2.25K.E

So new momentum is equal to 2.25K.E

NOW

Fractional change in kinetic energy is :-
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Fractional change in kinetic energy = K.E' _ K.E / K.E

Fractional change in kinetic energy = 2.25 K.E _ K.E / K.E

Fractional change in kinetic energy = 2.25 _1K.E / K.E (K.E will cancel out K.E )

Fractional change in kinetic energy = 1.25


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