A stone with weight $w$ is thrown vertically upward into the air from ground level with initial speed $v_0$. If a constant force $f$ due to air drag acts on the stone throughout its flight. The maximum height attained by the stone is
$h=\frac{v_0^2}{2 g\left(1-\frac{f}{w}\right)}$
$h=\frac{v_0^2}{2 g\left(1+\frac{f}{w}\right)}$
$h=\frac{v_0^2}{2 g\left(1+\frac{w}{f}\right)}$
$h=\frac{v_0^2}{2 g\left(1-\frac{w}{f}\right)}$
As shown in the figure, a particle of mass $10$ $kg$ is placed at a point $A$. When the particle is slightly displaced to its right, it starts moving and reaches the point $B$. The speed of the particle at $B$ is $x\, m / s$. (Take $\left. g =10\, m / s ^{2}\right)$ The value of $'x'$ to the nearest integer is.........
A wedge of mass $M = 4\,m$ lies on a frictionless plane. A particle of mass $m$ approaches the wedge with speed $v$. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by
A block of mass $m$ moving with speed $v$ compresses a spring through distance $x$ before its speed is halved. What is the value of spring constant ?
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 particle of mass $500 \,gm$ is moving in a straight line with velocity $v=b x^{5 / 2}$. The work done by the net force during its displacement from $x=0$ to $x =4 \,m$ is ...................$J$ (Take $b =0.25 \,m ^{-3 / 2} s ^{-1}$ )