Question

A ball takes $t$ second to fall from a height $h_1$ and $2t$ seconds to fall from a height $h_2$. Then $\frac{h_1}{h_2}$ is:

• A. $1.5$
• B. $1$
• C. $0.50$
• D. $0.25$

Answer 1

The correct option is D $0.25$

As we know that the time taken by an object to fall freely by height $h$ is $T=\sqrt{\frac{2h}{g}}$
So from the given condition we have
$t=\sqrt{\frac{2h_1}{g}}$ and $2t=\sqrt{\frac{2h_2}{g}}$
$\Rightarrow \frac{t}{2t}=\sqrt{\frac{h_1}{h_2}}$
$\Rightarrow \frac{h_1}{h_2}={\left(\frac{1}{2}\right)}^2=0.25$