Question

The rain drops falling from the sky neither injure us nor make holes on the ground because they move with:
(A) constant acceleration
(B) variable acceleration
(C) variable speed
(D) constant terminal velocity

Answer 1

Hint When raindrops are falling they experience air resistance and force due to this balances gravity, so acceleration stops while raindrops attain constant terminal velocity which is not high enough to cause damage. Damage is caused by sudden change in momentum. However tiny raindrops with not so much terminal velocity means that the momentum is not very high. So the change is also little.

Complete Step-by step answer
Firstly the impact of these droplets depends on sudden change in the momentum of the droplets when they hit any surface (be it the ground or our bare heads). Momentum is the product of the velocity and the mass of the body. Now we are lucky that these droplets are small and negligible in mass.
Whenever a body is free falling in a viscous fluid, it experiences a resistive force which acts opposite to the direction of travel of the body. This vicious force was given by Stokes, and is defined as:
\[F = 6\pi \eta rv\]
Then there is a force of gravity acting downwards and force of buoyancy acting upwards. Equating all these forces, we will achieve equilibrium. At equilibrium the velocity of a body moving through viscous fluid achieves a constant value called the terminal velocity. The value of this terminal velocity is given by
\[{v_t} = \dfrac{{2{r^2}(\rho - \sigma )g}}{{9\eta }}\]
r= radius of the spherical drops
ρ= density of water
σ= density of air
η= viscosity of fluid
Therefore a rain drop will not hurt us neither will it make holes on the ground because due to its very small size, it will have a very low terminal velocity.

correct option is D.

Note Different liquids will have different densities and viscosities, so the same object falling in a different medium will attain different terminal velocities. The terminal velocities of a body moving through a viscous medium are independent of the mass of that particular body.