Question

The ratios of the distance traversed, in successive intervals of time by a body, falling from rest, are

• A. 1 : 3 : 5 : 7 : 9.........
• B. 2 : 4 : 6 : 8 : 10 .........
• C. 1 : 4 : 7 : 10 : 13 .........
• D. None of the above

Answer 1

Answer: (A)

1 : 3 : 5 : 7 : 9.........

Answer 2

Initially, $u=0$
Distance travelled in $n$th second is given by
$h_{n}=u t+\frac{g}{2}(2 n-1)$
Distance travelled in 1st second
$h_{1}=0+\frac{g}{2}(2 \times 1-1)=\frac{g}{2}$
Distance travelled in 2nd second
$h_{2}=0+\frac{g}{2}(2 \times 2-1)$
$h_{2}=\frac{3 g}{2}$
Distance travelled in $3rd$ second
$h_{3}=0+\frac{g}{2}(2 \times 3-1)$
$h_{3}=\frac{5 g}{2}$
The ratio of distances
$h_{1}: h_{2}: h_{3}: h_{4}: h_{5} \ldots=1: 3: 5: 7$