Question

Single Correct Answer Type
A body of mass $m$ is projected horizontally with a velocity $v$ from the top of a tower of height $h$ and it reaches ground at a distance $x$ from the top of a tower. If a second body of mass $2m$ is projected horizontally from the top of a tower of height $2h$, it reaches the ground at a distance $2x$ from the tower. The horizontal velocity of second body is

• A. $v$
• B. $2v$
• C. $\sqrt{2}v$
• D. $\frac{v}{2}$

Answer 1

The correct option is C $\sqrt{2}v$

From above concept Range in x direction for body of mass $m$ projected with velocity $v$ from height $h$: :

$x=v\sqrt{\frac{2h}{g}}$
$\Rightarrow x^2=v^2\frac{2h}{g}$ .....(1)

Range in x direction for body of mass $2m$ projected with velocity $v^{\prime }$ from height $2h$:

$2x=v^{\prime }\sqrt{\frac{2\left(2h\right)}{g}}$
$\Rightarrow 4x^2=v^{\prime 2}\frac{4h}{g}$ .....(2)

Dividing equation (2) by equation (1)

$4=\frac{v^{\prime 2}}{v^2}2$
$\Rightarrow v^{\prime }=\sqrt{2}v$