Consider a drop of rain water having mass $1\,g$ falling from a height of $1\,km$. It hits the ground with a speed of $50\,m s^{-1}$. Take $g = 10\,m s^{-2}$. The work done by the $(i)$ gravitational force and the $(ii)$ resistive force of air is

$A$ truck of mass $M$ and a car of mass $\frac{M}{10}$ moving with the same momentum are brought to a halt by the application of the same braking force. The ratio of the distances travelled by the truck and the car before they come to a stop is

$A$ bullet of mass $4\,g$ is fired horizontally with a speed of $300\,m/s$ into a $0.8\,kg$ block of wood at rest on a table. If the coefficient of friction between the block and the table is $0.3$,how far will the block slide approximately (in $,m$)?

$A$ particle of mass $m$ is dropped from a height $h$ above the ground. At the same time,another particle of the same mass is thrown vertically upwards from the ground with a speed of $\sqrt{2gh}$. If they collide head-on completely inelastically,the time taken for the combined mass to reach the ground,in units of $\sqrt{\frac{h}{g}}$,is

$A$ particle of mass $m$ is projected from the ground with an initial speed $u_0$ at an angle $\alpha$ with the horizontal. At the highest point of its trajectory,it makes a completely inelastic collision with another identical particle,which was thrown vertically upward from the ground with the same initial speed $u_0$. The angle that the composite system makes with the horizontal immediately after the collision is :

$A$ $15 \,g$ ball is shot from a spring gun whose spring has a force constant of $600 \,N/m$. The spring is compressed by $5 \,cm$. The greatest possible horizontal range of the ball for this compression is .... $m$ $(g = 10 \,m/s^2)$ (in $.0$)