Raindrops of radius $1 \mathrm{mm}$ and mass $4 \mathrm{mg}$ are falling with a speed of $30 \mathrm{m} {\mathrm{s}}^{-1}$ on the head of a bald person. The drops splash on the head and come to rest. Assuming equivalently, that the drops cover a distance equal to their radii on the head, estimate the force exerted by each drop on the head.

Both the springs shown in the figure are unstretched. If the block is displaced by a distance $x$ and released, what will be the initial acceleration?

A small block $B$ is placed on another block $A$ of mass $5 \mathrm{kg}$ and length $20 \mathrm{cm}$. Initially, the block $B$ is near the right end of block $A$. A constant horizontal force of $10 \mathrm{N}$ is applied to the block $A$. All the surfaces are assumed frictionless. Find the time elapsed before the block $B$ separates from $A$.

A man has fallen into a ditch of width $d$ and two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in the figure. Show that the force (assumed equal for both the friends) exerted by each friend on the road increases as the man moves up. Find the force when the man is at a depth $h$.

The elevator shown in figure is descending with an acceleration of $2 \mathrm{m} {\mathrm{s}}^{-2}$. The mass of the block $A$ is $0.5 \mathrm{kg}$. What force is exerted by the block $A$ on the block $B$?

A pendulum bob of mass $50 \mathrm{g}$ is suspended from the ceiling of an elevator. Find the tension in the string if the elevator

$\left(a\right)$ goes up with the acceleration $1.2 \mathrm{m} {\mathrm{s}}^{-2}$,

$\left(b\right)$ goes up with deceleration $1.2 \mathrm{m} {\mathrm{s}}^{-2}$,

$\left(c\right)$ goes up with a uniform velocity,

$\left(d\right)$ goes down with the acceleration $1.2 \mathrm{m} {\mathrm{s}}^{-2}$,

$\left(e\right)$ goes down with the deceleration $1.2 \mathrm{m} {\mathrm{s}}^{-2}$ and 

$\left(f\right)$ goes down with uniform velocity.

A person is standing on a weighing machine placed on the floor of an elevator. The elevator starts going up with some acceleration, moves with uniform velocity for a while, and finally decelerates to stop. The maximum and the minimum weights recorded are $72 \mathrm{kg}$ and $60 \mathrm{kg}$. Assuming that the magnitudes of the acceleration and the deceleration are the same, find

(a) the true weight of the person,

(b) the magnitude of the acceleration. Take $g=9.9 \mathrm{m} {\mathrm{s}}^{-2}$.