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 S2 = 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/t2 = √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