Question

if movement of an object increase by 10% then its kinetic energy will be??

Answer 1

Given :-

If momentum changes by 10% then what will be its kinetic energy

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

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

New momentum is :-

P' = P +10%P

P' = P +10/100P

P' = P + 0.1P

P' = 1.1P

Now new kinetic energy will be

K.E' = P'^2/2m

Put value of P' in above relation

K.E' = (1.1P)^2 /2m ----------------------------------(2)

Divide equation 2 by equation 1

K.E'/K.E = (1.1 P)^2 /2m /P^2/2m

Or we can also write it as :-

K.E'/ K.E = (1.1 P)^2 /2m × 2m/P^2 ( 2m will cancel 2m , P^2 will cancel P^2 )

K.E'/K.E = (1.1)^2

1.1^2 = 1.21

So

K.E' /K.E = 1.21

K.E'= 1.21 K.E

So new kinetic energy is equal to 1.21 K.E

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

Fractional change in kinetic energy = 1.21K.E _ K.E/ K.E

Fractional change in kinetic energy = 1.21_1 K.E/K.E

Fractional change in kinetic energy = 0.21K.E/ K.E

Fractional change in kinetic energy = 0.21

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