A particle of mass $100\ g$ is thrown vertically upwards with a speed of $5\ m/s$. The work done by the force of gravity during the time the particle goes up is.....$J$

A rocket accelerates straight up by ejecting gas downwards. In a small time interval $\Delta t$, it ejects a gas of mass $\Delta m$ at a relative speed $u$. Calculate $KE$ of the entire system at $t + \Delta t$ and $t$ and show that the device that ejects gas does work $=(\frac {1}{2})\Delta mu^2$ in this time interval (negative gravity).

A bullet of mass $10 \;g$ leaves a rifle at an initial velocity of $1000 \;m/s$ and strikes the earth at the same level with a velocity of $500\; m / s$. The work done ($Joule$) in joule overcoming the resistance of air will be

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$  is proportional to

A mass of $M\ kg$ is suspended by a weightless string. The horizontal force that is displace it until the string makes an angle of $45^o $ with the initial vertical direction is

From a building two balls $A$ and $B$ are thrown such that $A$ is thrown upwards and $B$ downwards (both vertically). If $v_{A}$ and $v_{B}$ are their respective velocities on reaching the ground, then