Question

A body is falling freely under gravity. The distances covered by the body in first, second and third minute of its motion are in the ratio

• A. $ 1:4:9 $
• B. $ 1:2:3 $
• C. $ 1:3:5 $
• D. $ 1:5:6 $
• E. $ 1:5:13 $

Answer 1

Answer: (C)

Distance covered in a particular time is
$ {{s}_{n}}=u+\frac{1}{2}g(2n-1) $
$ \therefore $ $ {{s}_{1}}=0+\frac{1}{2}g(2\times 1-1)=\frac{g}{2} $
$ {{s}_{2}}=0+\frac{1}{2}g(2\times 2-1)=\frac{3}{2}g $
and $ {{s}_{3}}=0+\frac{1}{2}g(2\times 3-1)=\frac{5}{2}g $
Hence, the required ratio is
$ {{s}_{1}}:{{s}_{2}}:{{s}_{3}}=\frac{g}{2}:\frac{3}{2}g:\frac{5}{2}g $
$ = 1 : 3 : 5 $