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 these

Answer 1

Answer: (A)

Initially u = 0 Distance travelled in the nth second is given by
$h_n=u+\frac{g}{2}(2n-1)$
Distance travelled in the 1st second is
$h_1=0+\frac{g}{h}(2\times 1-1)=\frac{g}{2}$
Distance travelled in the 2nd second is
$h_2=0+\frac{g}{h}(2\times 2-1)=\frac{3g}{2}$
Distance travelled in 3rd second
$h_3=0+\frac{g}{2}(2\times 3-1)=\frac{5g}{2}$
The ratio of distances
$h_1:h_2:h_3:h_4:h_5:......=1:3:5:7:....$