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
$Mg$($\sqrt 2 $$+ 1)$
$Mg$$\sqrt 2 $
$\frac{{{\rm{Mg}}}}{{\sqrt 2 }}$
$Mg$($\sqrt 2 \;$$- 1)$
A lorry and a car moving with the same $K.E.$ are brought to rest by applying the same retarding force, then
If a shell fired from a cannon, explodes in mid air, then
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 bullet of mass $200\,g$ having initial kinetic energy $90\,J$ is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to $40\,J$ within 1s, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is $.....m$
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).