Question

Two bodies of masses m₁ and m₂ fall from heights h₁ and h₂ respectively. The ratio of their velocities, when they hit the ground is

• A. $h_2$
• B. $\sqrt{\frac{h_1}{h_2}}$
• C. $\frac{m_1{h}_1}{m_2{h}_2}$
• D. $\frac{{h_1}^2}{{h_2}^2}$

Answer 1

The correct option is B

$\sqrt{\frac{h_1}{h_2}}$

Step 1: Given data

$\text{Mass of particles}=m_1,m_2$

$\text{Heights}=h_1,h_2$

Step 2: To find

We have to determine the ratio of their velocity.

Step 3: Calculate the velocity of particle one

$$\begin{gathered} v_1=\sqrt{{u_1}^2+2g{h}_1} \\ =\sqrt{0^2+2g{h}_1} \\ =\sqrt{2g{h}_1} \end{gathered}$$

Here, $h_1$ is the height of tower one,$u_1$ is the initial velocity of particle one, $v_1$ is the final velocity of particle one and $g$ is the gravitational acceleration.

Step 4: Calculate the velocity of particle two

$$\begin{gathered} v_2=\sqrt{{u_2}^2+2g{h}_2} \\ =\sqrt{0^2+2g{h}_2} \\ =\sqrt{2g{h}_2} \end{gathered}$$

Here, $h_2$ is height of tower two,$u_2$ is initial velocity of particle two, $v_2$ is the final velocity of particle two and $g$ is the gravitational acceleration.

Step 5: Calculate the ratio

$$\begin{gathered} \frac{V_1}{V_2}=\sqrt{\frac{2g{h}_1}{2g{h}_2}} \\ =\sqrt{\frac{h_1}{h_2}} \end{gathered}$$

Hence, option(B) is correct.