$A$ body thrown vertically upwards from the ground reaches a maximum height $H$. The ratio of the velocities of the body at heights $\frac{3H}{4}$ and $\frac{8H}{9}$ from the ground is

$A$ balloon rises up with a constant net acceleration of $10\,m/s^2$. After $2\,s$,a particle drops from the balloon. After a further $2\,s$,match the following columns. (Take $g=10\,m/s^2$)

Column $I$	Column $II$
$(A)$ Height of particle from ground	$(p)$ $0$
$(B)$ Speed of particle	$(q)$ $10$ $SI$ unit
$(C)$ Displacement of particle	$(r)$ $40$ $SI$ unit
$(D)$ Acceleration of particle	$(s)$ $20$ $SI$ unit

Two balls are dropped from heights $h$ and $2h$ respectively from the Earth's surface. The ratio of the time taken by these balls to reach the Earth is

$A$ body is projected vertically upwards. The times corresponding to a specific height while ascending and while descending are $t_{1}$ and $t_{2}$ respectively. Then the velocity of projection is (where $g$ is acceleration due to gravity).

It is a common observation that rain clouds can be at about a kilometer altitude above the ground.
$(a)$ If a rain drop falls from such a height freely under gravity,what will be its speed? Also calculate in $km/h$ $(g = 10\, m/s^2)$.
$(b)$ $A$ typical rain drop is about $4\, mm$ in diameter. Momentum is mass $\times$ speed in magnitude. Estimate its momentum when it hits the ground.
$(c)$ Estimate the time required to flatten the drop.
$(d)$ Rate of change of momentum is force. Estimate how much force such a drop would exert on you.
$(e)$ Estimate the order of magnitude force on an umbrella. Typical lateral separation between two rain drops is $5\, cm$.
(Assume that the umbrella is circular and has a diameter of $1\, m$ and the cloth is not pierced through.)

$A$ body,thrown upwards with some velocity,reaches a maximum height of $20\,m$. Another body with double the mass thrown up with double the initial velocity will reach a maximum height of..........$m$.