- Home
- Standard 11
- Physics
Galileo's law of odd numbers: "The distances traversed, during equal intervals of time, by a body falltng from rest, stand to one another in the same ratio as the odd numbers begining with unity [namely, $1: 3: 5: 7 \ldots \ldots]$ Prove it.
Solution
Answer Let us divide the time interval of motion of an object under free fall into many equal intervals $\tau$ and find out the distances traversed during successive intervals of time. since initial velocity is zero, we have
$y=-\frac{1}{2} g t^{2}$
Using this equation, we can calculate the position of the object after different time intervals, $0, \tau, 2 \tau,$ 3 $\tau \ldots$ which are given in second column of Table. If we take $(-1 / 2) g \tau^{2}$ as $y_{0}-$ the position coordinate after first time interval $\tau$, then third column gives the positions in the unit of $y_{o} .$ The fourth column gives the distances traversed in successive ts. We find that the distances are in the simple ratio $1: 3: 5: 7: 9: 11 \ldots$ as shown in the last column. This law was established by Gallleo Galllet (1564-1642) who was the first to make quantitative studies of free fall.
