Question

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

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

Answer 1

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

Let $t$ be the descending time for travelling from $A$ to $B$ and $t_1$ be the descending time for travelling from $A$ to $C$.
So the distance travelled from $A$ to $B$ is
$S=\frac{1}{2}g{t}^2\Rightarrow t=\sqrt{\frac{2S}{g}}$
and from $A$ to $C$ is
$2S=\frac{1}{2}g{t}_1^2\Rightarrow t_1=\sqrt{\frac{4S}{g}}$
Hence, the ratio is given by
$\frac{t}{t_1}=\frac{1}{\sqrt{2}}$