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The ratio of the distances travelled by a freely falling body in the 1st1^{\text{st}}, 2nd2^{\text{nd}}, 3rd3^{\text{rd}} and 4th4^{\text{th}} second

A

1:2:3:41:2:3:4

B

1:4:9:161:4:9:16

C

1:3:5:71:3:5:7

D

1:1:1:11:1:1:1

Step-by-Step Solution

The distance travelled in the nthn^{\text{th}} second is given by Sn=u+a2(2n1)S_n = u + \frac{a}{2}(2n - 1). For a freely falling body, u=0u=0 and a=ga=g. Thus, Sn(2n1)S_n \propto (2n-1). For n=1,2,3,4n=1, 2, 3, 4, the ratios are (2(1)1):(2(2)1):(2(3)1):(2(4)1)=1:3:5:7(2(1)-1) : (2(2)-1) : (2(3)-1) : (2(4)-1) = 1 : 3 : 5 : 7.

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