Question

A ball dropped from a point $A$ falls down vertically to $C$, through the mid-point $B$. The descending time from $A$ to $B$ and that from $A$ to $C$ are in the ratio

• A. $1:1$
• B. $1:2$
• C. $1:3$
• D. $1:\sqrt{2}$
• E. $1:\sqrt{3}$

Answer 1

The correct option is D $1:\sqrt{2}$

Let the distance between point $A$ and $B$ is $s$
As, $u=0$, then
We know that, $s=ut+\frac{1}{2}g{t}^2$
For point $A$ to $B,s=\frac{1}{2}g{t}^2....\left(i\right)$
For point $A$ to $C,2s=\frac{1}{2}g{t}^2....\left(ii\right)$
On dividing Eq. (ii) by Eq. (i), we get
$\frac{t^2}{t^2}=\frac{1}{2}\Rightarrow \frac{t}{t^{\prime }}=\frac{1}{\sqrt{2}}=1:\sqrt{2}$.