Question

A body of mass m falls freely through a height h from top of a tower the velocity just before touching the ground is root 3/2 GH

Answer 1

Question:

A body of mass m falls freely through a height h from top of a tower the velocity just before touching the ground is root 3/2 GH. Find the air drag.

Given:

Mass of the body = m

Final velocity of the body =  $\sqrt{\frac{3gh}{2} }$

To find:

Drag force on the body due to air

Solution:

Let a be the acceleration due to the air drag acting on the body. As the air drag reduces the acceleration of body it is considered as negative

From equations of motion

        $v^2-u^2=2a_{eff}h$

        $v^2-u^2=2(g-a)h$

        $\frac{3gh}{2} =2(g-a)h$      

        $\frac{3g}{2} =2g-2a$    

        $2a=\frac{g}{2}$

        $a=\frac{g}{4}$

Force due to air drag  $=ma$

                                     $=m\times \frac{g}{4}$

                                     $=\frac{mg}{4}N$

Final answer:

The air drag on the body is  $\frac{mg}{4} N$