Question

The ratio of the distance travelled in successive seconds by a body during free fall is

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

Answer 1

The correct option is A $1:3:5:7:9:..........$

Initially $u=0$
Distance travelled in the $n^{th}$ second is given by
$h_n=u+\frac{g}{2}(2n-1)$
Distance travelled in the $1^{st}$ second is
$h_1=0+\frac{g}{2}(2\times 1-1)=\frac{g}{2}$
Distance travelled in the $2^{nd}$ second is
$h_2=0+\frac{g}{2}(2\times 2-1)=\frac{3g}{2}$
Distance travelled in the $3^{rd}$ second is
$h_2=0+\frac{g}{2}(2\times 3-1)=\frac{5g}{2}$
Ratios of the distance travelled in successive seconds is given by
$\frac{g}{2}:\frac{3g}{2}:\frac{5g}{2}\dots \dots =1:3:5:....$