- Home
- Standard 11
- Physics
गैलीलियो का विषम अंक संबंधित नियम : इस नियम के अनुसार "विरामावस्था से गिरती हुई किसी वस्तु द्वारा समान समय अंतरालों में चली गई दूरियाँ एक दूसरे से उसी अनुपात में होती हैं जिस अनुपात में एक से प्रारंभ होने वाले विषम अंक [अर्थात $1: 3: 5:$ $7, \ldots \ldots]$ "। इस कथन को सिद्ध कीजिए ।
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.
