Question

a body of mass m and velocity v if the mass is increased four times and velocity is decreased 2 times calculate ratio of their kinetic energy

Answer 1

First of all let's find out the initial kinetic energy:
Kinetic energy =1/2mv^2
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Now ,
They have increased the mass 4 times
therefore mass =4m
velocity is decreased twice
therefore velocity =v/2

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Let's find out the final kinetic energy:

K.E. =1/2 mv^2
=1/2 ×4m×(v/2)^2
=1/2 ×4m×v^2/4
=1/2 ×m×v^2
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Now let's find the ratio:

Initial kinetic energy/final kinetic energy=
1/2 mv^2/1/2mv^2
=1:1
Your final ratio =1:1

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.Hope you get it.