Question

Two identical bodies are dropped from two different heights h₁ and h₂, respectively. If the ratio of their final velocities is 3: 5, then the ratio of h₁
and h₂ is _________.

• A. 5 : 9
• B. 3 : 25
• C. 9 : 25
• D. 25 : 3

Answer 1

The correct option is C

9 : 25

Step 1, Given data

The ratio of the final velocity of the bodies = 3: 5

Heights are h₁ and h₂

Step 2, Finding the ratio of heights

We know,

The final velocity is given as

$$\begin{gathered} v=\sqrt{2gh} \\ Or,h=\frac{v^2}{2g} \end{gathered}$$

Now, according to the above equation, we can write

$\frac{h_1}{h_2}=\frac{{\displaystyle \frac{{v_1}^2}{2g}}}{{\displaystyle \frac{{v_2}^2}{2g}}}$

Or, $\frac{h_1}{h_2}=\frac{{v_1}^2}{{v_2}^2}$

Putting values

$\frac{h_1}{h_2}=\frac{3^2}{5^2}=\frac{9}{25}$

Therefore the ratio of the heights is 9: 25

Hence the correct option is (C)