Question

Water drops fall at regular intervals from a roof. At an instant when a drop is about to leave the roof, the separation between three successive drops below the roof are in what ratio?

Answer 1

Distance travelled in nth second
$S=u+\frac{1}{2}g(2n-1)$
$s_1=0+\frac{1}{2}g(2\times 1-1)=\frac{g}{2}$
$s_2=0+\frac{1}{2}g(2\times 2-1)=\frac{3g}{2}$
$s_3=0+\frac{1}{2}g(2\times 3-1)=\frac{5g}{2}$
Ratio $s_1:s_2:s_3=1:3:5$
Impulse = Change in momentum
$=P_2-P_1=mv-(-mu)=0.2\times 20\times 0.2\times 15=7kgm/s$