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Two particles A and B are dropped from the heights of 5 m and 20 m respectively. Then the ratio of time taken by A to that taken by B, to reach the ground is
1. 1 ∶ 4 
2. 2 ∶ 1
3. 1 ∶ 2
4. 1 ∶ 1

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Correct Answer - Option 3 : 1 ∶ 2

Concept used:

The formula from the 2nd equation of motion is, S = ut + (1/2) × at2

Here, S is dispacement, u is initial speed, t is the time taken and a is acceleration:

Now, as the particle is dropped from heights, then acceleration = gravitational speed

And, initial speed u will be equal to zero

∴ a = g, and S = (1/2) × gt2

Calculation:

Height S1 = 5 m and Height S= 20 m

S = (1/2) × gt2

We can speed is directly proportional to the square of the time taken:

So, we can write, S1/S2 = t12/t22

⇒ 5/20 = t12/t22

⇒ t1/t= √5/20 = √1/4 = 1/2

∴ The ratio of time taken by A to that taken by B, to reach the ground is 1 : 2

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