A stone is allowed to fall freely from rest. The ratio of the times taken to fall ….

Q: A stone is allowed to fall freely from rest. The ratio of the times taken to fall though the first metre and the second metre distance is
(a) √2 -1

(b) √2 + 1

(c) √2

(d) None of these

Ans: (b)

Sol: Using formula
\displaystyle S = ut + \frac{1}{2}gt^2

\displaystyle  1 =\frac{1}{2}gt_1^2

\displaystyle  1+1 =\frac{1}{2}g(t_1+t_2)^2

On dividing ,

\displaystyle  \frac{1}{2} = (\frac{t_1}{t_1+t_2})^2

\displaystyle \frac{1}{\sqrt 2} = \frac{t_1}{t_1+t_2}

\displaystyle \sqrt2 = \frac{t_1 + t_2}{t_1}

\displaystyle \sqrt2 = 1+\frac{t_2}{t_1}

\displaystyle  \sqrt2 - 1 = \frac{t_2}{t_1}

\displaystyle  \frac{t_1}{t_2} = \frac{1}{\sqrt2 - 1}

\displaystyle  \frac{t_1}{t_2} = \frac{1}{\sqrt2 - 1} \times \frac{\sqrt2 +1}{\sqrt2 +1}

\displaystyle  \frac{t_1}{t_2} = \sqrt2 + 1

Author: Rajesh Jha

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