A) 1 : 3 : 5 : 7 : 9.........
B) 2 : 4 : 6 : 8 : 10 .........
C) 1 : 4 : 7 : 10 : 13 .........
D) None of the above
Correct Answer: A
Solution :
Initially, u = 0 Distance travelled in nth second is given by \[{{h}_{n}}=ut+\frac{g}{2}(2n-1)\] Distance travelled in 1st second \[{{h}_{1}}=0+\frac{g}{2}+(2\times 1-1)=\frac{g}{2}\] Distance travelled in 2nd second \[{{h}_{2}}=0+\frac{g}{2}(2\times 2-1)\] \[{{h}_{2}}=\frac{3g}{2}\] Distance travelled in 3rd second \[{{h}_{3}}=0+\frac{g}{2}(2\times 3-1)\] \[{{h}_{3}}=\frac{5g}{2}\] The ratio of distances \[{{h}_{1}}:{{h}_{2}}:{{h}_{3}}:{{h}_{4}}:{{h}_{5}}\,...=1:3:5:7\,......\]
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