Question: A body is allowed to fall freely. The ratio of its displacement in 1,2 and 3 seconds is
• A
1:4:9
• B
1:2:3
• C
1:3:5
• D
1:9:25

Posted by: Arhaan on 02.02.2021

Here u=0 and s=1/2 gt^2 so the ratio is (1:4:9)
Ratio of displacement in 1s,2s and 3s=1^2:2^2:3^2=1:4:9
1:4:9 as displacement directly proportional to the square of time.
Option A = 1:4:9
As kinematical equation S=ut+1/2 at^2 In free fall it is Directly proportion to square of time S1:S2:S3= 1^2:2^2:3^2 =1:4:9
In free fall motion, displacement of body is directly proportional to the square of time. We get this from S=(1/2)gt². So the ratio of displacement for time 1:2:3::1²:2²:3² i. e. 1:4:9
If the question is ratio between 1st,2nd and 3rd second - 1:3:5 If the question is in 1sec:2sec:3sec - 1:4:9

The displacement varies as square of time for a freely falling body. Here, the 'g' remaining same, the ratio of the displacements of the body after 1, 2 and 3 seconds will be 1^2:2^2:3^2 = 1:4:9 . So, option A - 1:4:9 is correct

body falling freely , displacement is proportional to square of time d=gt^2/2 ,  This gives 1,4,9 . (squre of time)

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