Question

A body of mass $10kg$ is moving with a velocity $20m{s}^{-1}$. If the mass of the body is doubled and its velocity is halved, find the ratio of the initial kinetic energy to the final kinetic energy.

• A. $1:1$
• B. $1:2$
• C. $2:1$
• D. $1:4$

Answer 1

The correct option is C $2:1$

$K.E=0.5\times m\times v^2$
Mass is doubled that is became 2m where as velocity became v/2.
$K.E\left(new\right)=0.5\times 2m\times (v/2{)}^2=0.5\times m\times v^2(1/2)$
Hence ratio becomes $K.E=0.5\times m\times v^2:K.E=0.5\times m\times v^2\left(1/2\right)$
That is finally $2:1$.