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2.Motion in Straight Line
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A stone is allowed to fall freely from rest. The ratio of the times taken to fall through the first metre and the second metre distance is
A
$\sqrt{2}-1$
B
$\sqrt{2}+1$
C
$\sqrt{2}$
D
None of the above
Solution
(b)
$1=\frac{1}{2} g t_1^2$ or $t_1=\sqrt{\frac{2}{g}}$
$2=\frac{1}{2} g t^2 \quad$ or $\quad t=\sqrt{\frac{4}{g}}$
but $t_2=t-t_1=\sqrt{\frac{4}{g}}-\sqrt{\frac{2}{g}}$
$\therefore \frac{t_1}{t_2}=\frac{\sqrt{2 / g}}{\sqrt{4 / g}-\sqrt{2 / g}}$
$=\frac{\sqrt{2}}{2-\sqrt{2}}=\frac{\sqrt{2}(2+\sqrt{2})}{2}$
$=(\sqrt{2}+1)$
Standard 11
Physics
