Question

The ratio of distances traversed in successive intervals of time when a body falls freely under gravity from certain height is

• A. 1 : 2 : 3
• B. 1 : 5 : 9
• C. 1 : 3 : 5
• D. $\sqrt{1}:\sqrt{2}:\sqrt{3}$
• E. 1 : 4 : 9

Answer 1

Answer: (C)

Distance travelled by an object in a particular second.
$s_t=u+\frac{1}{2}g(2t-1)$
For $1s$
$s_1=0+\frac{1}{2}g...(i)$
For $2s$
$s_2=0+\frac{1}{2}g(4-1)$
$=\frac{1}{2}g\times 3...(ii)$
For $3s$
$s_3=0+\frac{1}{2}g(6-1)=\frac{1}{2}g\times 5...(iii)$
The ratio of distance
$s_1:s_2:s_3=\frac{1}{2}g:\frac{3}{2}g:\frac{5}{2}g$
$=1:3:5$