Question

When the momentum of a body is doubled, the kinetic energy is____

• A. doubled
• B. halved
• C. increased four times
• D. increased three times

Answer 1

The correct option is C increased four times

$P_{initial}=mv$

$P_{final}=2P=2mv$
Since mass of a given body is always constant, new velocity:
$v_{final}=2v$

So velocity gets doubled.

$K_{initial}=\frac{1}{2}m{v}^2$

$K_{final}=\frac{1}{2}m(2v{)}^2=4\frac{1}{2}m{v}^2$