SATHEE: Motion in a Straight Line

Motion in a Straight Line - Result Question 36

37. 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

(a) $h_{1} = \frac{h_{2}}{3} = \frac{h_{3}}{5}$

[2013]

(b) $h_{2} = 3 h_{1}$ and $h_{3} = 3 h_{2}$

(d) $h_{1} = 2 h_{2} = 3 h_{3}$

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Answer:

Correct Answer: 37. (a)

Solution:

(a) $∵ h = \frac{1}{2} g t^{2}$

$∴ h_{1} = \frac{1}{2} g (5)^{2} = 125$

$h_{1} + h_{2} = \frac{1}{2} g (10)^{2} = 500$

$\Rightarrow h_{2} = 375$

$h_{1} + h_{2} + h_{3} = \frac{1}{2} g (15)^{2} = 1125$

$\Rightarrow h_{3} = 625$

$h_{2} = 3 h_{1}, h_{3} = 5 h_{1}$

or $h_{1} = \frac{h_{2}}{3} = \frac{h_{3}}{5}$

The distance covered in time $t, 2 t, 3 t$ , etc. will be in the ratio of $1^{2} : 2^{2} : 3^{2}$ i.e., square of integers i.e., $h$ $\propto t^{2}$ .

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Motion in a Straight Line - Result Question 36

37. A stone falls freely under gravity. It covers distances h1,h2 and h3 in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h1,h2 and h3 is

Answer:

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37. 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