Question

A body falling from rest has a velocity ${}^{\prime }{v}^{\prime }$ after it falls through a distance ${}^{\prime }{h}^{\prime }$. The distance it has to fall down further, for its velocity to become $3v,$ is

• A. $4h$
• B. $8h$
• C. $3h$
• D. $6h$

Answer 1

The correct option is B $8h$

Answer (4)
Velocity of body after falling distance $h$
$v^2=2gh\Rightarrow h=\frac{v^2}{2g}\dots \left(i\right)$
Now, for velocity to become triple
$(3v{)}^2=2g{h}^{\prime }\Rightarrow h^{\prime }=\frac{9v^2}{2g}\dots \left(ii\right)$
Hence, required height $\Delta h=h^{\prime }-h$
$=\frac{9v^2}{2g}-\frac{v^2}{2g}=\frac{8v^2}{2g}=8h$