A child is swinging a swing. Minimum and maximum heights of swing from the earth's surface are $0.75\,m$ and $2\,m$ respectively. The maximum velocity of this swing is ............. $\mathrm{m}/ \mathrm{s}$

If a particle of mass $m$ is moving in a horizontal circle of radius $r$ with a centripetal force $( - k/{r^2})$, the total energy is

A cricket ball of mass $0.15\, kg$ is thrown vertically up by a bowling machine so that it rises to a maximum height of $20 \;m$ after leaving the machine. If the part pushing the ball applies a constant force $F$ on the ball and moves horizontally a distance of $0.2\, m$ while launching the ball, the value of $F($ in $N)$ is 

$\left(g=10\, m s^{-2}\right)$

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

A particle of mass $10\, g$ moves along a circle of  radius $6.4\, cm$ with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to $8 \times 10^{-4}\,J$ by the end of the second revolution after the beginning of the motion $?$ .............. $\mathrm{m} / \mathrm{s}^{2}$

The position $x$ of a particle moving along $x$-axis at time $(t)$ is given by the equation $t=\sqrt{x}+2$, where $x$ is in metres and $t$ in seconds. the work done by the force in first four seconds is .............. $J$