A stone falls freely under gravity. It covers distances $h_1, h_2$ and $h_3$ in the first 5 seconds, the…

A stone falls freely under gravity. It covers distances $h_1, h_2$ and $h_3$ in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between $h_1, h_2$ and $h_3$ is
  1. $h_1=2 h_2=3 h_3$
  2. $h_1=\frac{h_2}{3}=\frac{h_3}{5}$
  3. $h_2=3 h_1$ and $h_3=3 h_2$
  4. $h_1=h_2=h_3$

Solution

\(\begin{aligned} & h_1=\frac{1}{2} g t^2=\frac{1}{2} \times 10 \times 5^2=125 \\ & h_2=\frac{1}{2} \times 10 \times 10^2-\frac{1}{2} \times 10 \times 5^2=375 \\ & h_3=\frac{1}{2} \times 10 \times 15^2-\frac{1}{2} \times 10 \times 10^2=625 \end{aligned}\) Hence \(h_1=\frac{h_2}{3}=\frac{h_3}{5}\)

Asked in: NEET 2013 (All India)

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