Question

A rocket is moving up with a velocity $v$. If the velocity of this rocket is suddenly tripled, what will be the ratio of two kinetic energies ?

• A. $1$
• B. $1:9$
• C. $3$
• D. $1:3$

Answer 1

The correct option is B $1:9$

Initial velocity $=v$, then $v^{\prime }=3v$ (Tripled Velocity)
Initial kinetic energy $=\frac{1}{2}m{v}^2$
Final kinetic energy (K.E.)$=\frac{1}{2}m{v}^{\prime 2}=\frac{1}{2}m(3v{)}^2=9(\frac{1}{2}m{v}^2)$
$\therefore$ $(K.E.{)}_{initial}:(K.E.{)}_{final}=$$\frac{1}{2}m{v}^2:9\left(\frac{1}{2}m{v}^2\right)=1:9$