Question

Answer the question given in the attachment with full explanation .

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Answer 1

Answer :-

Required ratio of distance traversed in successive intervals of time is 1 : 3 : 5 [Option.c] .

Explanation :-

The distance travelled by a body in the 'nth' second of it's motion, is given by :-

Sₙₜₕ = u + a/2(2n - 1)

Let's take the succesive time interval as 1st sec, 2nd sec and 3rd sec . Initial velocity (u) of the body will be 0 m/s .

For 1st second :-

⇒ S₁ = 0 + g/2(2 × 1 - 1)

⇒ S₁ = g/2(1)

⇒ S₁ = 0.5g

For 2nd second :-

⇒ S₂ = 0 + g/2(2 × 2 - 1)

⇒ S₂ = g/2(3)

⇒ S₂ = 1.5g

For 3rd second :-

⇒ S₃ = 0 + g/2(2 × 3 - 1)

⇒ S₃ = g/2(5)

⇒ S₃ = 2.5g

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Now, ratio of distance traversed :-

= S₁ : S₂ : S₃

= 0.5g : 1.5g : 2.5g

= 2(0.5g) : 2(1.5g) : 2(2.5g)

= g : 3g : 5g

= 1 : 3 : 5

Answer 2

Answer:

Required ratio = 1:3:5

Explanation:

$\sf \tiny \red{ \boxed{ \frak{\purple{Your} \: \: \pink{Required} \: \: \green{Answer }}}} \downarrow$

$\sf \: \bigstar \: As \: we \: know \: that \\ \rightarrow \red{\boxed{ \bf \clubs\: Distance \: travelled \: in \: nth \: second = s _{n} \: = u + \frac{1}{2} a \: (2n - 1)}}$

Here u = 0 and a = g

So,

1st second -

$\sf s_1 = \frac{1}{2} g(2 \times 1 - 1) \\ ➥ \bf \: s_1 = \frac{1}{2} \: g$

2nd second-

$\sf \: s_2 = \frac{1}{2} g(2 \times 2 - 1) \\ ➥\bf s_2= \frac{3}{2} \: g$

3rd second-

$\sf \: s_3 = \frac{1}{2} g(2 \times 3 - 1) \\➥ \bf \: s_3 = \frac{5}{2} \: g$

$\sf \: Required \: ratio = \frac{1}{2} : \frac{3}{2} : \frac{5}{2} \\ \\ \pink{ \large{ \boxed{ \color{aqua} \frak{➥Required \: ratio = 1 : 3 : 5}}}}$

[Option 'c' supports the answer]