Question

A car is moving with a speed of $15km{h}^{-1}$ and another identical car is moving with a speed of $30km{h}^{-1}$. Ratio of their kinetic energies will be :

• A. 1 : 4
• B. 3 : 4
• C. 1 : 2
• D. 2 : 1

Answer 1

The correct option is A

1 : 4

Cars are identical which means mass of both the cars will be equal.

Let their masses be equal to $mKg$.

Let the speed of the cars be $v_1$ and $v_2$ respectively such that,

$v_1=15km{h}^{-1}$

$v_2=30km{h}^{-1}$

$\frac{K.E_1}{K.E_2}=\frac{\frac{1}{2}\times m\times v_1^2}{\frac{1}{2}\times m\times v_2^2}$

or , $\frac{K.E_1}{K.E_2}=\frac{(15{)}^2}{(30{)}^2}={\left(\frac{15}{30}\right)}^2={\left(\frac{1}{2}\right)}^2=\frac{1}{4}$

$\therefore$ Required ratio is 1 : 4