Question

A block is moving with a velocity of $10\text{m/s}$ and the observer is moving in the opposite direction at a speed of $20\text{m/s}$. Find the ratio of the kinetic energy of block w.r.t ground to the kinetic energy of block w.r.t observer.

• A. $\frac{1}{3}$
• B. $\frac{1}{9}$
• C. $\frac{1}{2}$
• D. value of mass is necessary to determine the ratio.

Answer 1

The correct option is B $\frac{1}{9}$

Let mass of block is $M$ and speed w.r.t ground is $V_g$ and w.r.t observer is $V_0$.
Kinetic energy with respect to ground $=K_g$
Given: $V_g=10\text{m/s}$
$K_g=\frac{1}{2}M{V}_g^2=\frac{1}{2}M\times {10}^2=50M$
Speed w.r.t observer $V_0=(10-(20\left)\right)\text{m/s}=30\text{m/s}$
Kinetic energy w.r.t observer $=K_0$
$K_0=\frac{1}{2}M{V}_0^2$
$K_0=\frac{1}{2}M\times {30}^2=450M$

$\frac{(K{)}_g}{(K{)}_0}=\frac{50}{450}=\frac{1}{9}$