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Motion in a Straight Line — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Straight Line2 Marks
Question
It is a common observation that rain clouds can be at about a kilometre altitude above the ground.A typical rain drop is about 4mm diameter. Momentum is mass x speed in magnitude. Estimate its momentum when it hits ground.
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Answer

Key concept: This problem can be solved by kinematic equations of motion and Newton’s second law that $\text{F}_\text{ext}=\frac{\text{dp}}{\text{dt}}$ will be used, where dp is change in momentum over time dt. Diameter of the drop (d) = 2r = 4mm Radius of the drop (r) = $2mm = 2 \times 10^{-3}m$ Mass of a rain drop (m) = v × p$=\frac{4}{3}\pi\text{r}^3\text{p}=\frac{4}{3}\times\frac{22}{7}\times(2\times10^{-3})^3\times10^3$
($\because$ Density of water = $10^3kg/m^2) \Rightarrow\text{m}=3.4\times10^{-5}\text{kg}$
Momentum of the rain drop (p) = mv$=3.4\times10^{-5}\times100\sqrt{2}$
$\Rightarrow\text{p}=4.7\times10^{-3}\text{kg-m/s}=5\times10^{-3}\text{kg-m/s}$

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