Question

If mass and velocity of a body are doubled, the kinetic energy of the body becomes

• A. Two times
• B. Four times
• C. Eight times
• D. Twelve times

Answer 1

The correct option is C Eight times

Kinetic energy of a body of mass m moving with velocity v, K.E. $=\frac{1}{2}m{v}^2$
When the mass and velocity are doubled:
$m^{\prime }=2m{v}^{\prime }=2v\Rightarrow \text{New kinetic energy,}K.E^{\prime }.=\frac{1}{2}{m}^{\prime }(v^{\prime }{)}^2\Rightarrow K.E^{\prime }=\frac{1}{2}(2m\left)\right(2v{)}^2\Rightarrow K.E^{\prime }=\frac{1}{2}\times 8m{v}^2=8\left(\frac{1}{2}m{v}^2\right)\Rightarrow K.E{.}^{\prime }=8K.E.$
Therefore, kinetic energy becomes 8 times.
Hence, the correct answer is option (c).