Power on $a$ mass is $P = (3t^2 -2t + 1)$ watt change in kinetic energy in $t = 2sec$ to $t = 4sec$ is :- .................... $\mathrm{J}$
$46$
$92$
$23$
$62$
Write the similarity between various forms of energy.
A body is projected from ground at an angle ${\theta _1}$ with the horizontal with kinetic energy $K$. What is the potential energy of the body, when the velocity makes an angle ${\theta _2}$ with the horizontal?
A simple pendulum of mass $200\, gm$ and length $100\, cm$ is moved aside till the string makes an angle of $60^o$ with the vertical. The kinetic and potential energies of the bob, when the string is inclined at $30^o$ to the vertical, are
A bolt of mass $0.3\; kg$ falls from the celling of an elevator moving down with an uniform speed of $7 \;m s ^{-1}$. It hits the floor of the elevator (length of the elevator $=3 \;m$ ) and does not rebound. What is the heat produced by the impact? Would your answer be different if the elevator were stationary?
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).