Question

If a body falling freely from rest has a velocity $v$ after it falls through a height, $h$ then the distance it has to fall further for its velocity to become double will be

• A. $3h$
• B. $6h$
• C. $8h$
• D. $10h$

Answer 1

The correct option is A

$3h$

Step 1: Given and to find

According to the question given that a body that is in a state of rest after falling from a height, $h$ this body achieves velocity, $v$

Determine the distance that the body must fall in order for its velocity to double.

Step 2: Equation of motion

1. When the body is considered to be falling from rest, it signifies the body's initial velocity is zero i.e, $u=0$
2. We know that the Acceleration of a body under free fall is due to gravity,$a=g$
3. We know that the third equation of motion $v^2=u^2+2as$…….(I)

Step 3: Finding the distance it has to fall further for its velocity to become double

1. Putting all given values in equation (I) we get,

$$\begin{gathered} \Rightarrow v^2=u^2+2as \\ \Rightarrow v^2=0^2+2gh \\ \Rightarrow v^2=2gh\Rightarrow v=\sqrt{2gh}.....\left(ii\right) \end{gathered}$$

2. Then, $v_1=\sqrt{2g{h}_1}.....\left(iii\right)$

By dividing (iii) by (ii) we get

$\Rightarrow \frac{v_1}{v}=\sqrt{\frac{h_1}{h}}$

$$\begin{gathered} \Rightarrow {\left(\frac{v_1}{v}\right)}^2=\frac{h_1}{h} \\ \Rightarrow {\left(2\right)}^2=\frac{h_1}{h} \\ \Rightarrow h_1=4h \end{gathered}$$

3. Thus, Height falling further = $4h-h=3h$

Hence, the correct option is (A) $3h$