Question

Calculate the decrease in the kinetic energy of a moving body if its velocity reduces to $(\frac{1}{3}{)}^{rd}$ of the initial velocity.

• A. same as the initial value.
• B. $(\frac{2}{3}{)}^{th}$ of the initial value.
• C. $(\frac{1}{9}{)}^{th}$ of the initial value.
• D. $(\frac{8}{9}{)}^{th}$ of the initial value.

Answer 1

The correct option is D $(\frac{8}{9}{)}^{th}$ of the initial value.

$K.E=0.5\times m\times v^2$
$K.E\left(new\right)=0.5\times m\times (v/3{)}^2$
$K.E\left(new\right)=0.5\times m\times v^2/9$
$K.E-K.E\left(new\right)=(1-1/9)0.5\times m\times v^2=\left(8/9\right)0.5\times m\times v^2$
Hence this is the decrease in Kinetic energy.